TSTP Solution File: SEU198+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU198+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 07:28:07 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU198+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.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 10:11:28 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(in_type, type, (
% 0.20/0.40 in: ( $i * $i ) > $o)).
% 0.20/0.40 tff(relation_rng_type, type, (
% 0.20/0.40 relation_rng: $i > $i)).
% 0.20/0.40 tff(tptp_fun_B_8_type, type, (
% 0.20/0.40 tptp_fun_B_8: $i)).
% 0.20/0.40 tff(tptp_fun_C_0_type, type, (
% 0.20/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(relation_rng_restriction_type, type, (
% 0.20/0.40 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_A_9_type, type, (
% 0.20/0.40 tptp_fun_A_9: $i)).
% 0.20/0.40 tff(subset_type, type, (
% 0.20/0.40 subset: ( $i * $i ) > $o)).
% 0.20/0.40 tff(relation_type, type, (
% 0.20/0.40 relation: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40 tff(14,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!9, B!8)))) | in(C, A!9)))) | (~(subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~((~((~subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!9, B!8)))) | in(C, A!9)))) | (~(subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~((~subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9)) | ![C: $i] : ((~in(C, relation_rng(relation_rng_restriction(A!9, B!8)))) | in(C, A!9)))) | (~(subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)))))) | (subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), A))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t116_relat_1')).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ~((~relation(B!8)) | subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9)),
% 0.20/0.40 inference(or_elim,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~(subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))))) | subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~(subset(relation_rng(relation_rng_restriction(A!9, B!8)), A!9) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))))) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~(in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8))))))) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8)))) | (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (~(in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 41, 39])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (relation(B!8)),
% 0.20/0.41 inference(or_elim,[status(thm)],[31])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C))))))) <=> ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.41 tff(52,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t115_relat_1')).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.41 tff(55,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (in(A, B) & in(A, relation_rng(C)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))) | ((~relation(B!8)) | (in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))) | (~relation(B!8)) | (in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))) | ((~relation(B!8)) | (in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_rng(relation_rng_restriction(B, C))) <=> (~((~in(A, B)) | (~in(A, relation_rng(C)))))))) | (~relation(B!8)) | (in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(relation_rng_restriction(A!9, B!8))) <=> (~((~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), A!9)) | (~in(tptp_fun_C_0(A!9, relation_rng(relation_rng_restriction(A!9, B!8))), relation_rng(B!8))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 57, 44, 43])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------