TSTP Solution File: SEU321+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 07:28:54 EDT 2022
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n023.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Sep 3 12:24:33 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.31 Usage: tptp [options] [-file:]file
% 0.11/0.31 -h, -? prints this message.
% 0.11/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.31 -m, -model generate model.
% 0.11/0.31 -p, -proof generate proof.
% 0.11/0.31 -c, -core generate unsat core of named formulas.
% 0.11/0.31 -st, -statistics display statistics.
% 0.11/0.31 -t:timeout set timeout (in second).
% 0.11/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.31 -<param>:<value> configuration parameter and value.
% 0.11/0.31 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(in_type, type, (
% 0.17/0.37 in: ( $i * $i ) > $o)).
% 0.17/0.37 tff(tptp_fun_B_6_type, type, (
% 0.17/0.37 tptp_fun_B_6: $i)).
% 0.17/0.37 tff(tptp_fun_C_7_type, type, (
% 0.17/0.37 tptp_fun_C_7: $i)).
% 0.17/0.37 tff(subset_complement_type, type, (
% 0.17/0.37 subset_complement: ( $i * $i ) > $i)).
% 0.17/0.37 tff(the_carrier_type, type, (
% 0.17/0.37 the_carrier: $i > $i)).
% 0.17/0.37 tff(tptp_fun_A_5_type, type, (
% 0.17/0.37 tptp_fun_A_5: $i)).
% 0.17/0.37 tff(element_type, type, (
% 0.17/0.37 element: ( $i * $i ) > $o)).
% 0.17/0.37 tff(powerset_type, type, (
% 0.17/0.37 powerset: $i > $i)).
% 0.17/0.37 tff(empty_set_type, type, (
% 0.17/0.37 empty_set: $i)).
% 0.17/0.37 tff(empty_type, type, (
% 0.17/0.37 empty: $i > $o)).
% 0.17/0.37 tff(v1_membered_type, type, (
% 0.17/0.37 v1_membered: $i > $o)).
% 0.17/0.37 tff(v2_membered_type, type, (
% 0.17/0.37 v2_membered: $i > $o)).
% 0.17/0.37 tff(v3_membered_type, type, (
% 0.17/0.37 v3_membered: $i > $o)).
% 0.17/0.37 tff(v4_membered_type, type, (
% 0.17/0.37 v4_membered: $i > $o)).
% 0.17/0.37 tff(v5_membered_type, type, (
% 0.17/0.37 v5_membered: $i > $o)).
% 0.17/0.37 tff(one_sorted_str_type, type, (
% 0.17/0.37 one_sorted_str: $i > $o)).
% 0.17/0.37 tff(empty_carrier_type, type, (
% 0.17/0.37 empty_carrier: $i > $o)).
% 0.17/0.37 tff(1,assumption,(the_carrier(A!5) = empty_set), introduced(assumption)).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (empty(the_carrier(A!5)) <=> empty(empty_set)),
% 0.17/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (empty(empty_set) <=> empty(the_carrier(A!5))),
% 0.17/0.37 inference(symmetry,[status(thm)],[2])).
% 0.17/0.37 tff(4,plain,
% 0.17/0.37 (empty(empty_set) <=> empty(empty_set)),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(5,axiom,(((((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)) & v4_membered(empty_set)) & v5_membered(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_membered')).
% 0.17/0.37 tff(6,plain,
% 0.17/0.37 ((((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)) & v4_membered(empty_set)),
% 0.17/0.37 inference(and_elim,[status(thm)],[5])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 (((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)) & v3_membered(empty_set)),
% 0.17/0.37 inference(and_elim,[status(thm)],[6])).
% 0.17/0.37 tff(8,plain,
% 0.17/0.37 ((empty(empty_set) & v1_membered(empty_set)) & v2_membered(empty_set)),
% 0.17/0.37 inference(and_elim,[status(thm)],[7])).
% 0.17/0.37 tff(9,plain,
% 0.17/0.37 (empty(empty_set) & v1_membered(empty_set)),
% 0.17/0.37 inference(and_elim,[status(thm)],[8])).
% 0.17/0.37 tff(10,plain,
% 0.17/0.37 (empty(empty_set)),
% 0.17/0.37 inference(and_elim,[status(thm)],[9])).
% 0.17/0.37 tff(11,plain,
% 0.17/0.37 (empty(empty_set)),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.17/0.37 tff(12,plain,
% 0.17/0.37 (empty(the_carrier(A!5))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.17/0.37 tff(13,plain,
% 0.17/0.37 ((((~empty_carrier(A!5)) & one_sorted_str(A!5)) & (element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))) <=> ((~empty_carrier(A!5)) & one_sorted_str(A!5) & element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(14,plain,
% 0.17/0.37 (((~(~element(B!6, powerset(the_carrier(A!5))))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6)))))) <=> (element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(15,plain,
% 0.17/0.37 ((~(~((~empty_carrier(A!5)) & one_sorted_str(A!5)))) <=> ((~empty_carrier(A!5)) & one_sorted_str(A!5))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(16,plain,
% 0.17/0.37 (((~(~((~empty_carrier(A!5)) & one_sorted_str(A!5)))) & ((~(~element(B!6, powerset(the_carrier(A!5))))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))) <=> (((~empty_carrier(A!5)) & one_sorted_str(A!5)) & (element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6)))))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[15, 14])).
% 0.17/0.37 tff(17,plain,
% 0.17/0.37 (((~(~((~empty_carrier(A!5)) & one_sorted_str(A!5)))) & ((~(~element(B!6, powerset(the_carrier(A!5))))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))) <=> ((~empty_carrier(A!5)) & one_sorted_str(A!5) & element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[16, 13])).
% 0.17/0.37 tff(18,plain,
% 0.17/0.37 ((~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(19,plain,
% 0.17/0.37 ((~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(20,axiom,(~![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l40_tops_1')).
% 0.17/0.37 tff(21,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.17/0.37 tff(23,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.17/0.37 tff(24,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.17/0.37 tff(25,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.17/0.37 tff(26,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.17/0.37 tff(27,plain,
% 0.17/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.17/0.37 tff(28,plain,
% 0.17/0.37 ((~empty_carrier(A!5)) & one_sorted_str(A!5) & element(B!6, powerset(the_carrier(A!5))) & (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.17/0.37 tff(29,plain,
% 0.17/0.37 (one_sorted_str(A!5)),
% 0.17/0.37 inference(and_elim,[status(thm)],[28])).
% 0.17/0.37 tff(30,plain,
% 0.17/0.37 (~empty_carrier(A!5)),
% 0.17/0.37 inference(and_elim,[status(thm)],[28])).
% 0.17/0.37 tff(31,plain,
% 0.17/0.37 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(32,plain,
% 0.17/0.37 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.17/0.37 tff(33,plain,
% 0.17/0.37 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(34,plain,
% 0.17/0.37 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.17/0.37 tff(35,plain,
% 0.17/0.37 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(36,plain,
% 0.17/0.37 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(37,plain,
% 0.17/0.37 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.17/0.37 tff(38,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.17/0.37 tff(39,plain,
% 0.17/0.37 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.17/0.37 tff(40,plain,
% 0.17/0.37 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.17/0.37 tff(41,plain,(
% 0.17/0.37 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.17/0.37 inference(skolemize,[status(sab)],[40])).
% 0.17/0.37 tff(42,plain,
% 0.17/0.37 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.17/0.37 tff(43,plain,
% 0.17/0.37 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.17/0.37 tff(44,plain,
% 0.17/0.37 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(45,plain,
% 0.17/0.37 ((empty_carrier(A!5) | (~empty(the_carrier(A!5))) | (~one_sorted_str(A!5))) <=> (empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(46,plain,
% 0.17/0.37 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!5) | (~empty(the_carrier(A!5))) | (~one_sorted_str(A!5)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5)))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[45])).
% 0.17/0.37 tff(47,plain,
% 0.17/0.37 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!5) | (~empty(the_carrier(A!5))) | (~one_sorted_str(A!5)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[46, 44])).
% 0.17/0.37 tff(48,plain,
% 0.17/0.37 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!5) | (~empty(the_carrier(A!5))) | (~one_sorted_str(A!5)))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(49,plain,
% 0.17/0.37 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!5) | (~one_sorted_str(A!5)) | (~empty(the_carrier(A!5)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.17/0.37 tff(50,plain,
% 0.17/0.37 (~empty(the_carrier(A!5))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[49, 43, 30, 29])).
% 0.17/0.37 tff(51,plain,
% 0.17/0.37 ($false),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[50, 12])).
% 0.17/0.37 tff(52,plain,(~(the_carrier(A!5) = empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.37 tff(53,plain,
% 0.17/0.37 (^[A: $i] : refl(((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(54,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[53])).
% 0.17/0.37 tff(55,plain,
% 0.17/0.37 (^[A: $i] : rewrite(((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(56,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.17/0.37 tff(57,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[56, 54])).
% 0.17/0.37 tff(58,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(59,plain,
% 0.17/0.37 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((~in(C, B)) => in(C, subset_complement(A, B))) <=> (in(C, B) | in(C, subset_complement(A, B)))), ((element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))) <=> (element(C, A) => (in(C, B) | in(C, subset_complement(A, B)))))), rewrite((element(C, A) => (in(C, B) | in(C, subset_complement(A, B)))) <=> (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))), ((element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))) <=> (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))), (![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))) <=> ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))), ((element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))) <=> (element(B, powerset(A)) => ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))), rewrite((element(B, powerset(A)) => ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))) <=> ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))), ((element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))) <=> ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))), (![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))) <=> ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))), (((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))))) <=> ((~(A = empty_set)) => ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))), rewrite(((~(A = empty_set)) => ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))) <=> ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))), (((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))))) <=> ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(60,plain,
% 0.17/0.37 (![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B)))))) <=> ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.17/0.37 tff(61,axiom,(![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t50_subset_1')).
% 0.17/0.37 tff(62,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.17/0.37 tff(63,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.17/0.37 tff(64,plain,(
% 0.17/0.37 ![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(skolemize,[status(sab)],[63])).
% 0.17/0.37 tff(65,plain,
% 0.17/0.37 (![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.17/0.37 tff(66,plain,
% 0.17/0.37 (((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B)))))) <=> ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | (the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B)))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(67,plain,
% 0.17/0.37 (((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | in(C, subset_complement(the_carrier(A!5), B)) | (~element(C, the_carrier(A!5)))))) <=> ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B)))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(68,plain,
% 0.17/0.37 (((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | in(C, subset_complement(the_carrier(A!5), B)) | (~element(C, the_carrier(A!5))))))) <=> ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[67])).
% 0.17/0.37 tff(69,plain,
% 0.17/0.37 (((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | in(C, subset_complement(the_carrier(A!5), B)) | (~element(C, the_carrier(A!5))))))) <=> ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | (the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B)))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[68, 66])).
% 0.17/0.37 tff(70,plain,
% 0.17/0.37 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | in(C, subset_complement(the_carrier(A!5), B)) | (~element(C, the_carrier(A!5))))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(71,plain,
% 0.17/0.37 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) | (the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.37 tff(72,plain,
% 0.17/0.37 ((the_carrier(A!5) = empty_set) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.17/0.37 tff(73,plain,
% 0.17/0.37 (![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[72, 52])).
% 0.17/0.37 tff(74,assumption,(~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))), introduced(assumption)).
% 0.17/0.37 tff(75,assumption,(![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))), introduced(assumption)).
% 0.17/0.37 tff(76,plain,
% 0.17/0.37 (element(B!6, powerset(the_carrier(A!5)))),
% 0.17/0.37 inference(and_elim,[status(thm)],[28])).
% 0.17/0.37 tff(77,plain,
% 0.17/0.37 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | (~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(78,plain,
% 0.17/0.37 (((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B!6) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)))) <=> ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(79,plain,
% 0.17/0.37 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B!6) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[78])).
% 0.17/0.37 tff(80,plain,
% 0.17/0.37 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B!6) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | (~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6)))),
% 0.17/0.37 inference(transitivity,[status(thm)],[79, 77])).
% 0.17/0.37 tff(81,plain,
% 0.17/0.37 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B!6) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(82,plain,
% 0.17/0.37 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | (~element(B!6, powerset(the_carrier(A!5)))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.17/0.37 tff(83,plain,
% 0.17/0.37 ($false),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[82, 76, 75, 74])).
% 0.17/0.37 tff(84,plain,((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | ![C: $i] : (in(C, B) | (~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B))))) | ![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.37 tff(85,plain,
% 0.17/0.37 (![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[84, 73])).
% 0.17/0.38 tff(86,assumption,(![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))), introduced(assumption)).
% 0.17/0.38 tff(87,assumption,(~in(C!7, B!6)), introduced(assumption)).
% 0.17/0.38 tff(88,plain,
% 0.17/0.38 ((~(in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6)))) <=> (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> in(C!7, B!6))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(89,plain,
% 0.17/0.38 (~((~element(C!7, the_carrier(A!5))) | (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6))))),
% 0.17/0.38 inference(and_elim,[status(thm)],[28])).
% 0.17/0.38 tff(90,plain,
% 0.17/0.38 (~(in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> (~in(C!7, B!6)))),
% 0.17/0.38 inference(or_elim,[status(thm)],[89])).
% 0.17/0.38 tff(91,plain,
% 0.17/0.38 (in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> in(C!7, B!6)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[90, 88])).
% 0.17/0.38 tff(92,plain,
% 0.17/0.38 ((~in(C!7, subset_complement(the_carrier(A!5), B!6))) | in(C!7, B!6) | (~(in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> in(C!7, B!6)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(93,plain,
% 0.17/0.38 ((~in(C!7, subset_complement(the_carrier(A!5), B!6))) | in(C!7, B!6)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.17/0.38 tff(94,plain,
% 0.17/0.38 (~in(C!7, subset_complement(the_carrier(A!5), B!6))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[93, 87])).
% 0.17/0.38 tff(95,plain,
% 0.17/0.38 (element(C!7, the_carrier(A!5))),
% 0.17/0.38 inference(or_elim,[status(thm)],[89])).
% 0.17/0.38 tff(96,plain,
% 0.17/0.38 (((~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))) | ((~element(C!7, the_carrier(A!5))) | in(C!7, subset_complement(the_carrier(A!5), B!6)) | in(C!7, B!6))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))) | (~element(C!7, the_carrier(A!5))) | in(C!7, subset_complement(the_carrier(A!5), B!6)) | in(C!7, B!6))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(97,plain,
% 0.17/0.38 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))) | ((~element(C!7, the_carrier(A!5))) | in(C!7, subset_complement(the_carrier(A!5), B!6)) | in(C!7, B!6))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(98,plain,
% 0.17/0.38 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))) | (~element(C!7, the_carrier(A!5))) | in(C!7, subset_complement(the_carrier(A!5), B!6)) | in(C!7, B!6)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.17/0.38 tff(99,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[98, 95, 94, 87, 86])).
% 0.17/0.38 tff(100,plain,((~![C: $i] : ((~element(C, the_carrier(A!5))) | in(C, subset_complement(the_carrier(A!5), B!6)) | in(C, B!6))) | in(C!7, B!6)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(101,plain,
% 0.17/0.38 (in(C!7, B!6)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[100, 85])).
% 0.17/0.38 tff(102,plain,
% 0.17/0.38 (in(C!7, subset_complement(the_carrier(A!5), B!6)) | (~in(C!7, B!6)) | (~(in(C!7, subset_complement(the_carrier(A!5), B!6)) <=> in(C!7, B!6)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(103,plain,
% 0.17/0.38 (in(C!7, subset_complement(the_carrier(A!5), B!6)) | (~in(C!7, B!6))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[102, 91])).
% 0.17/0.38 tff(104,plain,
% 0.17/0.38 (in(C!7, subset_complement(the_carrier(A!5), B!6))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[103, 101])).
% 0.17/0.38 tff(105,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : refl(((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(106,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[105])).
% 0.17/0.38 tff(107,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(B, subset_complement(A, C)) & in(B, C)) <=> (~((~in(B, C)) | (~in(B, subset_complement(A, C)))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> (~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))))), rewrite((~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C)))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))))), rewrite(((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(108,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.38 tff(109,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(110,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(111,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[110])).
% 0.17/0.38 tff(112,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_subset_1')).
% 0.17/0.38 tff(113,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.17/0.38 tff(114,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.17/0.38 tff(115,plain,(
% 0.17/0.38 ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.17/0.38 inference(skolemize,[status(sab)],[114])).
% 0.17/0.38 tff(116,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.17/0.38 tff(117,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.17/0.38 tff(118,plain,
% 0.17/0.38 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(C!7, B!6)) | (~element(B!6, powerset(the_carrier(A!5)))) | (~in(C!7, subset_complement(the_carrier(A!5), B!6))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~in(C!7, B!6)) | (~element(B!6, powerset(the_carrier(A!5)))) | (~in(C!7, subset_complement(the_carrier(A!5), B!6))))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(119,plain,
% 0.17/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(C!7, B!6)) | (~element(B!6, powerset(the_carrier(A!5)))) | (~in(C!7, subset_complement(the_carrier(A!5), B!6))))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(120,plain,
% 0.17/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~in(C!7, B!6)) | (~element(B!6, powerset(the_carrier(A!5)))) | (~in(C!7, subset_complement(the_carrier(A!5), B!6)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.17/0.38 tff(121,plain,
% 0.17/0.38 ((~in(C!7, B!6)) | (~in(C!7, subset_complement(the_carrier(A!5), B!6)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[120, 76, 117])).
% 0.17/0.38 tff(122,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[121, 104, 101])).
% 0.17/0.38 % SZS output end Proof
%------------------------------------------------------------------------------