TSTP Solution File: SET372+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET372+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:06:36 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET372+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 04:53:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_X_0_type, type, (
% 0.19/0.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.40 tff(power_set_type, type, (
% 0.19/0.40 power_set: $i > $i)).
% 0.19/0.40 tff(intersection_type, type, (
% 0.19/0.40 intersection: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_B_3_type, type, (
% 0.19/0.40 tptp_fun_B_3: $i)).
% 0.19/0.40 tff(tptp_fun_A_4_type, type, (
% 0.19/0.40 tptp_fun_A_4: $i)).
% 0.19/0.40 tff(subset_type, type, (
% 0.19/0.40 subset: ( $i * $i ) > $o)).
% 0.19/0.40 tff(equal_set_type, type, (
% 0.19/0.40 equal_set: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.40 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.40 tff(14,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))))) | (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,(
% 0.19/0.40 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.40 inference(skolemize,[status(sab)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,assumption,((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))), introduced(assumption)).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 16, 42])).
% 0.19/0.41 tff(45,plain,(~((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (((~((~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(power_set(A!4), power_set(B!3)))) | member(X, power_set(intersection(A!4, B!3)))))) | (~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))))) | (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[50, 16])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))))) | (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[54, 27])).
% 0.19/0.42 tff(56,assumption,(~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))), introduced(assumption)).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 53])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 49])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[70, 16])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))))) | ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 27])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[76, 39])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[78, 56])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[81, 77])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[89, 73])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[91, 64])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 92, 90])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (~((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 16])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~(subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)))))) | ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 ((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[101, 27])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[103, 82])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))) | (~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4))) | subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | (~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 ((~((~subset(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), A!4)) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[109, 100])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ((~![X: $i] : ((~member(X, tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(X, A!4))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[113, 92, 110])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 ((~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3)))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))), B!3))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[115, 114, 96, 69])).
% 0.19/0.44 tff(117,plain,((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ((~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))) | subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((~(subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))), power_set(intersection(A!4, B!3))))))) | subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 (subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[119, 47])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(126,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.44 tff(128,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[127])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) <=> (~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) <=> (~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))) <=> (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(134,axiom,(~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI21')).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 133])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[138, 133])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (~![A: $i, B: $i] : equal_set(power_set(intersection(A, B)), intersection(power_set(A), power_set(B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.19/0.45 tff(142,plain,(
% 0.19/0.45 ~equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[141])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 ((~(equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) <=> (~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))))) | equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 ((~(equal_set(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) <=> (~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))))) | ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[144, 132])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 ((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))))) | (~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 ((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | (~subset(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[147, 120])).
% 0.19/0.45 tff(149,assumption,((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))), introduced(assumption)).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[150, 16, 149])).
% 0.19/0.45 tff(152,plain,(~((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (((~((~subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3)))) | ![X: $i] : ((~member(X, power_set(intersection(A!4, B!3)))) | member(X, intersection(power_set(A!4), power_set(B!3)))))) | (~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))))) | (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 ((~(subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))))) | subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (subset(power_set(intersection(A!4, B!3)), intersection(power_set(A!4), power_set(B!3))) | (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[156, 148])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) | ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))))) | ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[161, 41])).
% 0.19/0.46 tff(163,assumption,(~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))))), introduced(assumption)).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[158, 163])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3))) <=> (~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))))) | ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[160, 164])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 ((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[165, 41])).
% 0.19/0.46 tff(167,assumption,(~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))), introduced(assumption)).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[168, 16])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(intersection(A!4, B!3), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))))))) | ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 ((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[172, 27])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 163])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 ((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 ((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 (![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[180, 171])).
% 0.19/0.46 tff(182,assumption,(member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))), introduced(assumption)).
% 0.19/0.46 tff(183,assumption,(![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))), introduced(assumption)).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[186, 167, 183, 182])).
% 0.19/0.47 tff(188,plain,((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) | (~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[188, 181, 167])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.19/0.47 tff(192,assumption,((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))), introduced(assumption)).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 16, 192])).
% 0.19/0.47 tff(195,plain,(~((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, B!3)))) | (~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))) | (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[199, 191])).
% 0.19/0.47 tff(201,assumption,(~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))), introduced(assumption)).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[202, 27, 201])).
% 0.19/0.47 tff(204,plain,(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[206, 200])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 ((~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[208, 207, 166])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.19/0.48 tff(212,plain,
% 0.19/0.48 (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[211, 29])).
% 0.19/0.48 tff(213,plain,
% 0.19/0.48 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.19/0.48 tff(215,plain,
% 0.19/0.48 (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[214, 20])).
% 0.19/0.48 tff(216,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[218, 215])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.19/0.48 tff(222,assumption,(~(member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))), introduced(assumption)).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(224,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[223, 39, 222])).
% 0.19/0.48 tff(225,plain,(member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[227, 221])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 (((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))) <=> ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(230,plain,
% 0.19/0.48 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 ((~![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[231, 181, 228, 217])).
% 0.19/0.48 tff(233,plain,(((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))) | member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(power_set(A!4), power_set(B!3)))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[233, 157])).
% 0.19/0.48 tff(235,assumption,(~(member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))), introduced(assumption)).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[236, 39, 235])).
% 0.19/0.48 tff(238,plain,(member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))))) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (~((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[240, 234])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 ((~member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(B!3, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), B!3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[199, 245])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[206, 246])).
% 0.19/0.49 tff(248,plain,
% 0.19/0.49 ((~((~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(B!3))))) | (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[208, 247])).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (~member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[248, 162])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(A!4)) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))) | (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[210, 249])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[250, 29])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 ((~(subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), A!4) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))))) | (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[213, 251])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (~((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[252, 20])).
% 0.19/0.49 tff(254,plain,
% 0.19/0.49 (member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[216, 253])).
% 0.19/0.49 tff(255,plain,
% 0.19/0.49 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[218, 253])).
% 0.19/0.49 tff(256,plain,
% 0.19/0.49 ((~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), B!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[220, 255])).
% 0.19/0.49 tff(257,plain,
% 0.19/0.49 (~member(tptp_fun_X_0(A!4, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3)))), intersection(A!4, B!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[227, 256])).
% 0.19/0.49 tff(258,plain,
% 0.19/0.49 (member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[174, 157])).
% 0.19/0.49 tff(259,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), power_set(intersection(A!4, B!3))) <=> subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3)))) | subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[176, 258])).
% 0.19/0.49 tff(260,plain,
% 0.19/0.49 (subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[259, 173])).
% 0.19/0.49 tff(261,plain,
% 0.19/0.49 ((~((~subset(tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3))))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[179, 260])).
% 0.19/0.49 tff(262,plain,
% 0.19/0.49 (![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(A!4), power_set(B!3)), power_set(intersection(A!4, B!3))))) | member(X, intersection(A!4, B!3)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[261, 171])).
% 0.19/0.49 tff(263,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[231, 262, 257, 254])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------