TSTP Solution File: NUM531+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM531+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 13:10:18 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM531+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 11:40:47 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(isCountable0_type, type, (
% 0.21/0.39 isCountable0: $i > $o)).
% 0.21/0.39 tff(slcrc0_type, type, (
% 0.21/0.39 slcrc0: $i)).
% 0.21/0.39 tff(tptp_fun_W0_1_type, type, (
% 0.21/0.39 tptp_fun_W0_1: $i)).
% 0.21/0.39 tff(aSet0_type, type, (
% 0.21/0.39 aSet0: $i > $o)).
% 0.21/0.39 tff(aElementOf0_type, type, (
% 0.21/0.39 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_W1_0_type, type, (
% 0.21/0.39 tptp_fun_W1_0: $i > $i)).
% 0.21/0.39 tff(isFinite0_type, type, (
% 0.21/0.39 isFinite0: $i > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))) <=> (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~(W0 = slcrc0)))) <=> (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~(W0 = slcrc0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~![W0: $i] : ((~(W0 = slcrc0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.39 tff(11,plain,(
% 0.21/0.39 ~((~(W0!1 = slcrc0)) | (~(aSet0(W0!1) & isCountable0(W0!1))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (W0!1 = slcrc0),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (slcrc0 = W0!1),
% 0.21/0.39 inference(symmetry,[status(thm)],[12])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (isCountable0(slcrc0) <=> isCountable0(W0!1)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (isCountable0(W0!1) <=> isCountable0(slcrc0)),
% 0.21/0.39 inference(symmetry,[status(thm)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (aSet0(W0!1) & isCountable0(W0!1)),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (isCountable0(W0!1)),
% 0.21/0.39 inference(and_elim,[status(thm)],[16])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (isCountable0(slcrc0)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (^[W0: $i] : rewrite((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (^[W0: $i] : refl((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (^[W0: $i] : rewrite((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (^[W0: $i] : trans(monotonicity(rewrite(((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) <=> ((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))), rewrite(((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)) <=> ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))), ((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))), rewrite((((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))), ((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (^[W0: $i] : rewrite((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))) <=> (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))) <=> ![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0)))) <=> ![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(31,axiom,(![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefEmp')).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.40 tff(33,plain,(
% 0.21/0.40 ![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[32])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 20])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))) <=> ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~((~((slcrc0 = slcrc0) | (~aSet0(slcrc0)) | aElementOf0(tptp_fun_W1_0(slcrc0), slcrc0))) | (~((~(slcrc0 = slcrc0)) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0))))))))) <=> (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~((slcrc0 = slcrc0) | (~aSet0(slcrc0)) | aElementOf0(tptp_fun_W1_0(slcrc0), slcrc0))) | (~((~(slcrc0 = slcrc0)) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))))))) <=> ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~((slcrc0 = slcrc0) | (~aSet0(slcrc0)) | aElementOf0(tptp_fun_W1_0(slcrc0), slcrc0))) | (~((~(slcrc0 = slcrc0)) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))))))) <=> ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~((slcrc0 = slcrc0) | (~aSet0(slcrc0)) | aElementOf0(tptp_fun_W1_0(slcrc0), slcrc0))) | (~((~(slcrc0 = slcrc0)) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (~((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (((~aSet0(slcrc0)) | (~![W1: $i] : (~aElementOf0(W1, slcrc0)))) | aSet0(slcrc0)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (aSet0(slcrc0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (^[W0: $i] : refl(((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & isCountable0(W0)) <=> (~((~aSet0(W0)) | (~isCountable0(W0))))), ((~(aSet0(W0) & isCountable0(W0))) <=> (~(~((~aSet0(W0)) | (~isCountable0(W0))))))), rewrite((~(~((~aSet0(W0)) | (~isCountable0(W0))))) <=> ((~aSet0(W0)) | (~isCountable0(W0)))), ((~(aSet0(W0) & isCountable0(W0))) <=> ((~aSet0(W0)) | (~isCountable0(W0))))), (((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ((~isFinite0(W0)) | ((~aSet0(W0)) | (~isCountable0(W0)))))), rewrite(((~isFinite0(W0)) | ((~aSet0(W0)) | (~isCountable0(W0)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))), (((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (^[W0: $i] : rewrite(((aSet0(W0) & isCountable0(W0)) => (~isFinite0(W0))) <=> ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~isFinite0(W0))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.40 tff(54,axiom,(![W0: $i] : ((aSet0(W0) & isCountable0(W0)) => (~isFinite0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mCountNFin')).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.40 tff(57,plain,(
% 0.21/0.40 ![W0: $i] : ((~isFinite0(W0)) | (~(aSet0(W0) & isCountable0(W0))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[56])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (isFinite0(slcrc0) <=> isFinite0(slcrc0)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(61,axiom,(isFinite0(slcrc0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEmpFin')).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (isFinite0(slcrc0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))) | ((~isFinite0(slcrc0)) | (~aSet0(slcrc0)) | (~isCountable0(slcrc0)))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))) | (~isFinite0(slcrc0)) | (~aSet0(slcrc0)) | (~isCountable0(slcrc0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))) | ((~isFinite0(slcrc0)) | (~aSet0(slcrc0)) | (~isCountable0(slcrc0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | (~isCountable0(W0)))) | (~isFinite0(slcrc0)) | (~aSet0(slcrc0)) | (~isCountable0(slcrc0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 ((~aSet0(slcrc0)) | (~isCountable0(slcrc0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (~isCountable0(slcrc0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[66, 46])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[67, 18])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------