TSTP Solution File: NUM414+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : Sun Sep 18 13:09:33 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 10:11:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_A_15_type, type, (
% 0.13/0.39 tptp_fun_A_15: $i)).
% 0.13/0.39 tff(tptp_fun_B_16_type, type, (
% 0.13/0.39 tptp_fun_B_16: $i)).
% 0.13/0.39 tff(ordinal_subset_type, type, (
% 0.13/0.39 ordinal_subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(ordinal_type, type, (
% 0.13/0.39 ordinal: $i > $o)).
% 0.13/0.39 tff(proper_subset_type, type, (
% 0.13/0.39 proper_subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (((~(~ordinal(A!15))) & (~((~ordinal(B!16)) | (~((~proper_subset(A!15, B!16)) & (~(A!15 = B!16)) & (~proper_subset(B!16, A!15))))))) <=> (ordinal(A!15) & (~((~ordinal(B!16)) | (~((~proper_subset(A!15, B!16)) & (~(A!15 = B!16)) & (~proper_subset(B!16, A!15)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~proper_subset(A, B)) & (~(A = B))) & (~proper_subset(B, A))))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~proper_subset(A, B)) & (~(A = B))) & (~proper_subset(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t50_ordinal1')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~proper_subset(A, B)) & (~(A = B)) & (~proper_subset(B, A))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (ordinal(A!15) & (~((~ordinal(B!16)) | (~((~proper_subset(A!15, B!16)) & (~(A!15 = B!16)) & (~proper_subset(B!16, A!15))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~((~ordinal(B!16)) | (~((~proper_subset(A!15, B!16)) & (~(A!15 = B!16)) & (~proper_subset(B!16, A!15)))))),
% 0.13/0.39 inference(and_elim,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (ordinal(B!16)),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (ordinal(A!15)),
% 0.13/0.39 inference(and_elim,[status(thm)],[12])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.40 tff(26,plain,(
% 0.13/0.40 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[25])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (((ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)) | (~ordinal(A!15)) | (~ordinal(B!16))) <=> ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)) | (~ordinal(A!15)) | (~ordinal(B!16)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)) | (~ordinal(A!15)) | (~ordinal(B!16)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[31, 29])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)) | (~ordinal(A!15)) | (~ordinal(B!16)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (ordinal_subset(B!16, A!15) <=> subset(B!16, A!15)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[34, 28, 15, 14])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)) | (~ordinal(B!16)) | (~ordinal(A!15))) <=> ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)) | (~ordinal(B!16)) | (~ordinal(A!15)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)) | (~ordinal(B!16)) | (~ordinal(A!15)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)) | (~ordinal(B!16)) | (~ordinal(A!15)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (ordinal_subset(A!15, B!16) <=> subset(A!15, B!16)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[41, 28, 15, 14])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,axiom,(![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_xboole_0')).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[49])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))) | (proper_subset(A!15, B!16) <=> (~((~subset(A!15, B!16)) | (A!15 = B!16))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (proper_subset(A!15, B!16) <=> (~((~subset(A!15, B!16)) | (A!15 = B!16)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~proper_subset(A!15, B!16)) & (~(A!15 = B!16)) & (~proper_subset(B!16, A!15))),
% 0.13/0.40 inference(or_elim,[status(thm)],[13])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (~proper_subset(A!15, B!16)),
% 0.13/0.40 inference(and_elim,[status(thm)],[55])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 ((~(proper_subset(A!15, B!16) <=> (~((~subset(A!15, B!16)) | (A!15 = B!16))))) | proper_subset(A!15, B!16) | ((~subset(A!15, B!16)) | (A!15 = B!16))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((~(proper_subset(A!15, B!16) <=> (~((~subset(A!15, B!16)) | (A!15 = B!16))))) | ((~subset(A!15, B!16)) | (A!15 = B!16))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 ((~subset(A!15, B!16)) | (A!15 = B!16)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (~(A!15 = B!16)),
% 0.13/0.40 inference(and_elim,[status(thm)],[55])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 ((~((~subset(A!15, B!16)) | (A!15 = B!16))) | (~subset(A!15, B!16)) | (A!15 = B!16)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 ((~((~subset(A!15, B!16)) | (A!15 = B!16))) | (~subset(A!15, B!16))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (~subset(A!15, B!16)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~(ordinal_subset(A!15, B!16) <=> subset(A!15, B!16))) | (~ordinal_subset(A!15, B!16)) | subset(A!15, B!16)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~(ordinal_subset(A!15, B!16) <=> subset(A!15, B!16))) | (~ordinal_subset(A!15, B!16))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (~ordinal_subset(A!15, B!16)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 42])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))))), rewrite((ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite((ordinal_subset(A, B) | ordinal_subset(B, A)) <=> (ordinal_subset(B, A) | ordinal_subset(A, B))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))))), rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.40 tff(74,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','connectedness_r1_ordinal1')).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.40 tff(77,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[76])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ((ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15) | (~ordinal(A!15)) | (~ordinal(B!16))) <=> ((~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15) | (~ordinal(A!15)) | (~ordinal(B!16)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15) | (~ordinal(A!15)) | (~ordinal(B!16)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15))),
% 0.20/0.41 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15) | (~ordinal(A!15)) | (~ordinal(B!16)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(B!16)) | ordinal_subset(A!15, B!16) | ordinal_subset(B!16, A!15)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (ordinal_subset(B!16, A!15)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[85, 79, 15, 14, 66])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B))))) | (proper_subset(B!16, A!15) <=> (~((~subset(B!16, A!15)) | (B!16 = A!15))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (proper_subset(B!16, A!15) <=> (~((~subset(B!16, A!15)) | (B!16 = A!15)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 52])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (~proper_subset(B!16, A!15)),
% 0.20/0.41 inference(and_elim,[status(thm)],[55])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((~(proper_subset(B!16, A!15) <=> (~((~subset(B!16, A!15)) | (B!16 = A!15))))) | proper_subset(B!16, A!15) | ((~subset(B!16, A!15)) | (B!16 = A!15))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 ((~(proper_subset(B!16, A!15) <=> (~((~subset(B!16, A!15)) | (B!16 = A!15))))) | ((~subset(B!16, A!15)) | (B!16 = A!15))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ((~subset(B!16, A!15)) | (B!16 = A!15)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((B!16 = A!15) <=> (A!15 = B!16)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((A!15 = B!16) <=> (B!16 = A!15)),
% 0.20/0.41 inference(symmetry,[status(thm)],[93])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~(A!15 = B!16)) <=> (~(B!16 = A!15))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (~(B!16 = A!15)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 95])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~((~subset(B!16, A!15)) | (B!16 = A!15))) | (~subset(B!16, A!15)) | (B!16 = A!15)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (~subset(B!16, A!15)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 96, 92])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~(ordinal_subset(B!16, A!15) <=> subset(B!16, A!15))) | (~ordinal_subset(B!16, A!15)) | subset(B!16, A!15)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~(ordinal_subset(B!16, A!15) <=> subset(B!16, A!15))) | (~ordinal_subset(B!16, A!15))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 86, 35])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------