%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL139-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:51:19 AM UTC 2026
% Result : Unsatisfiable 1.97s 1.14s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 80 unt; 9 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,negated_conjecture,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
implies(x,not(truth)) != not(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
fof(f8,definition,
! [X0] : sF0(X0) = implies(truth,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X0] : implies(truth,X0) = sF0(X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF1(X1,X2,X0) = implies(implies(X1,X2),implies(X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : implies(implies(X1,X2),implies(X0,X2)) = sF1(X1,X2,X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = implies(implies(X0,X1),sF1(X1,X2,X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : implies(implies(X0,X1),sF1(X1,X2,X0)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : truth = sF2(X0,X1,X2),
inference(definition_folding,[],[f3,f14,f12]) ).
fof(f16,definition,
! [X0,X1] : sF3(X0,X1) = implies(implies(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f17,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0,X1] : sF3(X0,X1) = sF3(X1,X0),
inference(definition_folding,[],[f4,f17,f17]) ).
fof(f19,definition,
! [X0,X1] : sF4(X0,X1) = implies(not(X0),not(X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f20,plain,
! [X0,X1] : implies(not(X0),not(X1)) = sF4(X0,X1),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X0,X1] : sF5(X0,X1) = implies(sF4(X0,X1),implies(X1,X0)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f22,plain,
! [X0,X1] : implies(sF4(X0,X1),implies(X1,X0)) = sF5(X0,X1),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0,X1] : truth = sF5(X0,X1),
inference(definition_folding,[],[f6,f22,f20]) ).
fof(f24,definition,
sF6 = not(truth),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f25,plain,
not(truth) = sF6,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF7 = implies(x,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f27,plain,
implies(x,sF6) = sF7,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF8 = not(x),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f29,plain,
not(x) = sF8,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
sF7 != sF8,
inference(definition_folding,[],[f7,f29,f27,f25]) ).
fof(f31,plain,
! [X0,X1] : truth = implies(sF4(X0,X1),implies(X1,X0)),
inference(forward_demodulation,[],[f23,f22]) ).
fof(f32,plain,
! [X0,X1] : implies(implies(X1,X0),X0) = sF3(X0,X1),
inference(forward_demodulation,[],[f18,f17]) ).
fof(f33,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),sF1(X1,X2,X0)),
inference(forward_demodulation,[],[f15,f14]) ).
fof(f34,plain,
! [X0] : implies(truth,X0) = X0,
inference(forward_demodulation,[],[f10,f9]) ).
fof(f35,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(forward_demodulation,[],[f31,f20]) ).
fof(f36,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(forward_demodulation,[],[f32,f17]) ).
fof(f37,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(forward_demodulation,[],[f33,f12]) ).
fof(f43,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f35,f34]) ).
fof(f45,plain,
! [X0] : truth = implies(implies(not(X0),sF6),X0),
inference(forward_demodulation,[],[f43,f25]) ).
fof(f86,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f36,f34]) ).
fof(f193,plain,
! [X0] : truth = implies(sF7,implies(implies(sF6,X0),implies(x,X0))),
inference(superposition,[],[f37,f27]) ).
fof(f214,plain,
! [X0] : truth = implies(implies(X0,x),implies(sF7,implies(X0,sF6))),
inference(superposition,[],[f37,f27]) ).
fof(f220,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f37,f35]) ).
fof(f235,plain,
! [X0] : truth = implies(implies(x,X0),implies(implies(X0,sF6),sF7)),
inference(superposition,[],[f37,f27]) ).
fof(f236,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f37,f34]) ).
fof(f269,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f236,f34]) ).
fof(f283,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f220,f34]) ).
fof(f426,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f269,f86]) ).
fof(f435,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f34,f269]) ).
fof(f439,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f435,f34]) ).
fof(f527,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f426,f439]) ).
fof(f536,plain,
! [X0,X1] : truth = implies(truth,implies(implies(truth,X1),implies(X0,X1))),
inference(superposition,[],[f37,f527]) ).
fof(f552,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(forward_demodulation,[],[f536,f34]) ).
fof(f560,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f552,f34]) ).
fof(f611,plain,
! [X0] : truth = implies(sF7,implies(truth,implies(x,implies(X0,sF6)))),
inference(superposition,[],[f193,f560]) ).
fof(f637,plain,
! [X0] : truth = implies(sF7,implies(x,implies(X0,sF6))),
inference(forward_demodulation,[],[f611,f34]) ).
fof(f869,plain,
truth = implies(truth,implies(sF7,implies(implies(not(x),sF6),sF6))),
inference(superposition,[],[f214,f45]) ).
fof(f893,plain,
truth = implies(sF7,implies(implies(not(x),sF6),sF6)),
inference(forward_demodulation,[],[f869,f34]) ).
fof(f897,plain,
truth = implies(sF7,implies(implies(sF6,not(x)),not(x))),
inference(forward_demodulation,[],[f893,f36]) ).
fof(f899,plain,
truth = implies(sF7,implies(implies(sF6,sF8),sF8)),
inference(forward_demodulation,[],[f897,f29]) ).
fof(f927,plain,
truth = implies(implies(x,implies(not(sF6),sF6)),implies(truth,sF7)),
inference(superposition,[],[f235,f45]) ).
fof(f943,plain,
truth = implies(implies(x,implies(not(sF6),sF6)),sF7),
inference(forward_demodulation,[],[f927,f34]) ).
fof(f994,plain,
implies(truth,sF7) = implies(implies(sF7,implies(x,implies(not(sF6),sF6))),implies(x,implies(not(sF6),sF6))),
inference(superposition,[],[f36,f943]) ).
fof(f1004,plain,
implies(truth,sF7) = implies(truth,implies(x,implies(not(sF6),sF6))),
inference(forward_demodulation,[],[f994,f637]) ).
fof(f1008,plain,
implies(truth,sF7) = implies(x,implies(not(sF6),sF6)),
inference(forward_demodulation,[],[f1004,f34]) ).
fof(f1010,plain,
sF7 = implies(x,implies(not(sF6),sF6)),
inference(forward_demodulation,[],[f1008,f34]) ).
fof(f2673,plain,
! [X0,X1] : truth = implies(truth,implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f283,f560]) ).
fof(f2875,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f2673,f34]) ).
fof(f2888,plain,
! [X0] : truth = implies(not(truth),X0),
inference(superposition,[],[f2875,f34]) ).
fof(f2930,plain,
truth = implies(not(x),sF7),
inference(superposition,[],[f2875,f1010]) ).
fof(f2983,plain,
truth = implies(sF8,sF7),
inference(forward_demodulation,[],[f2930,f29]) ).
fof(f2986,plain,
! [X0] : truth = implies(sF6,X0),
inference(forward_demodulation,[],[f2888,f25]) ).
fof(f2994,plain,
implies(truth,sF7) = implies(implies(sF7,sF8),sF8),
inference(superposition,[],[f36,f2983]) ).
fof(f3017,plain,
sF7 = implies(implies(sF7,sF8),sF8),
inference(forward_demodulation,[],[f2994,f34]) ).
fof(f3026,plain,
truth = implies(sF7,implies(truth,sF8)),
inference(superposition,[],[f899,f2986]) ).
fof(f3086,plain,
truth = implies(sF7,sF8),
inference(forward_demodulation,[],[f3026,f34]) ).
fof(f3912,plain,
sF7 = implies(truth,sF8),
inference(forward_demodulation,[],[f3017,f3086]) ).
fof(f3913,plain,
sF7 = sF8,
inference(forward_demodulation,[],[f3912,f34]) ).
fof(f3914,plain,
sF7 != sF7,
inference(superposition,[],[f30,f3913]) ).
fof(f3936,plain,
$false,
inference(trivial_inequality_removal,[],[f3914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL139-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 15:23:26 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.97/1.14 % (3093204)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.97/1.14 % (3093249)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2727866902:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.97/1.14 % (3093245)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1983818463:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.97/1.14 % (3093248)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3634994199:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.97/1.14 % (3093249)First to succeed.
% 1.97/1.14 % (3093249)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3093204"
% 1.97/1.14 % (3093247)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1432077151:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.97/1.14 % (3093246)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3438852:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.97/1.14 % (3093250)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=816177572:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.97/1.14 % (3093251)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1668669082:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.97/1.14 % (3093248)Also succeeded, but the first one will report.
% 1.97/1.14 % (3093251)Also succeeded, but the first one will report.
% 1.97/1.14 % (3093250)Also succeeded, but the first one will report.
% 1.97/1.14 % (3093249)Refutation found. Thanks to Tanya!
% 1.97/1.14 % SZS status Unsatisfiable for theBenchmark
% 1.97/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.33 % (3093249)------------------------------
% 2.75/1.33 % (3093249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.33 % (3093249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.33 % (3093249)CaDiCaL version: 2.1.3
% 2.75/1.33 % (3093249)Termination reason: Refutation
% 2.75/1.33 % (3093249)Time elapsed: 0.037 s
% 2.75/1.33 % (3093249)Peak memory usage: 89 MB
% 2.75/1.33 % (3093249)Instructions burned: 114 (million)
% 2.75/1.33 % (3093249)------------------------------
% 2.75/1.33 % (3093249)------------------------------
% 2.75/1.33 % (3093204)Success in time 0.298 s
% 2.75/1.33 % Vampire exiting
%------------------------------------------------------------------------------