%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 11:51:20 AM UTC 2026
% Result : Unsatisfiable 6.90s 2.02s
% Output : Refutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 51 unt; 6 def)
% Number of atoms : 51 ( 50 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; 9 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/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,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox/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,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
fof(f14,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f15,plain,
! [X0,X1] : big_hat(X0,X1) = not(implies(implies(not(X0),not(X1)),not(X1))),
inference(definition_unfolding,[],[f9,f8]) ).
fof(f16,plain,
implies(implies(not(x),not(y)),not(y)) != not(not(implies(implies(not(x),not(y)),not(y)))),
inference(definition_unfolding,[],[f14,f15,f8]) ).
fof(f17,definition,
sF0 = not(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f18,plain,
not(x) = sF0,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF1 = not(y),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f20,plain,
not(y) = sF1,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF2 = implies(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f22,plain,
implies(sF0,sF1) = sF2,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF3 = implies(sF2,sF1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f24,plain,
implies(sF2,sF1) = sF3,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF4 = not(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f26,plain,
not(sF3) = sF4,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF5 = not(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f28,plain,
not(sF4) = sF5,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
sF3 != sF5,
inference(definition_folding,[],[f16,f28,f26,f24,f20,f22,f20,f18,f24,f20,f22,f20,f18]) ).
fof(f48,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f3,f6]) ).
fof(f52,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f60,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f52,f1]) ).
fof(f62,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f48,f1]) ).
fof(f70,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f97,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(superposition,[],[f3,f60]) ).
fof(f103,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f60]) ).
fof(f105,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f103,f1]) ).
fof(f109,plain,
! [X2,X0,X1] : truth = implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f97,f1]) ).
fof(f387,plain,
! [X0,X1] : truth = implies(implies(implies(X0,X0),X1),implies(X0,X1)),
inference(superposition,[],[f109,f70]) ).
fof(f447,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(forward_demodulation,[],[f387,f105]) ).
fof(f468,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f447,f1]) ).
fof(f552,plain,
! [X0,X1] : truth = implies(truth,implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f62,f468]) ).
fof(f581,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f552,f1]) ).
fof(f608,plain,
! [X0,X1] : truth = implies(truth,implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[],[f62,f581]) ).
fof(f635,plain,
! [X0,X1] : truth = implies(not(not(X0)),implies(X1,X0)),
inference(forward_demodulation,[],[f608,f1]) ).
fof(f648,plain,
! [X0] : truth = implies(not(not(X0)),X0),
inference(superposition,[],[f635,f1]) ).
fof(f701,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(superposition,[],[f6,f648]) ).
fof(f728,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f701,f1]) ).
fof(f743,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(superposition,[],[f4,f728]) ).
fof(f768,plain,
! [X0] : not(not(X0)) = implies(implies(not(not(X0)),X0),X0),
inference(forward_demodulation,[],[f743,f1]) ).
fof(f776,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f768,f648]) ).
fof(f779,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f776,f1]) ).
fof(f783,plain,
sF3 = not(sF4),
inference(superposition,[],[f779,f26]) ).
fof(f796,plain,
sF3 = sF5,
inference(forward_demodulation,[],[f783,f28]) ).
fof(f797,plain,
$false,
inference(forward_subsumption_resolution,[],[f796,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:24:09 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.64/1.79 % (1371587)Input is clausal, will run a generic CNF schedule.
% 5.64/1.79 % (1371693)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2315720047:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.64/1.79 % (1371695)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2544652584:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.64/1.79 % (1371698)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2151250353:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.64/1.79 % (1371696)lrs+10_1_sil=8000:sp=occurrence:random_seed=2416722688:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.64/1.79 % (1371694)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2291515585:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.64/1.79 % (1371697)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2530539088:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.64/1.79 % (1371699)dis-21_1_sil=8000:lcm=predicate:random_seed=4131788429:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.64/1.79 % (1371699)Refutation not found, incomplete strategy
% 5.64/1.79 % (1371699)------------------------------
% 5.64/1.79 % (1371699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.79 % (1371699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.79 % (1371699)CaDiCaL version: 2.1.3
% 5.64/1.79 % (1371699)Termination reason: Refutation not found, incomplete strategy
% 5.64/1.79 % (1371699)Time elapsed: 0.001 s
% 5.64/1.79 % (1371699)Peak memory usage: 88 MB
% 5.64/1.79 % (1371696)Instruction limit reached!
% 5.64/1.79 % (1371696)------------------------------
% 5.64/1.79 % (1371696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.79 % (1371696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.79 % (1371696)CaDiCaL version: 2.1.3
% 5.64/1.79 % (1371696)Termination reason: Instruction limit
% 5.64/1.79 % (1371696)Termination phase: Saturation
% 5.64/1.79 % (1371696)Time elapsed: 0.066 s
% 5.64/1.79 % (1371696)Peak memory usage: 89 MB
% 5.64/1.79 % (1371696)Instructions burned: 107 (million)
% 5.64/1.79 % (1371697)Instruction limit reached!
% 5.64/1.79 % (1371697)------------------------------
% 5.64/1.79 % (1371697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.79 % (1371697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.79 % (1371697)CaDiCaL version: 2.1.3
% 5.64/1.79 % (1371697)Termination reason: Instruction limit
% 5.64/1.79 % (1371697)Termination phase: Saturation
% 5.64/1.79 % (1371697)Time elapsed: 0.072 s
% 5.64/1.79 % (1371697)Peak memory usage: 89 MB
% 5.64/1.79 % (1371697)Instructions burned: 114 (million)
% 5.64/1.79 % (1371698)Instruction limit reached!
% 5.64/1.79 % (1371698)------------------------------
% 5.64/1.79 % (1371698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.79 % (1371698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.79 % (1371698)CaDiCaL version: 2.1.3
% 5.64/1.79 % (1371698)Termination reason: Instruction limit
% 5.64/1.79 % (1371698)Termination phase: Saturation
% 5.64/1.79 % (1371698)Time elapsed: 0.103 s
% 5.64/1.79 % (1371698)Peak memory usage: 89 MB
% 5.64/1.79 % (1371698)Instructions burned: 180 (million)
% 5.64/1.79 % (1371721)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3851076848:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.64/1.79 % (1371721)Refutation not found, incomplete strategy
% 5.64/1.79 % (1371721)------------------------------
% 5.64/1.79 % (1371721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.79 % (1371721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.79 % (1371721)CaDiCaL version: 2.1.3
% 5.64/1.79 % (1371721)Termination reason: Refutation not found, incomplete strategy
% 5.64/1.79 % (1371721)Time elapsed: 0.002 s
% 5.64/1.79 % (1371721)Peak memory usage: 88 MB
% 5.64/1.79 % (1371721)Instructions burned: 1 (million)
% 5.64/1.79 % (1371720)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1843596352:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.90/2.01 % (1371720)Refutation not found, incomplete strategy
% 6.90/2.01 % (1371720)------------------------------
% 6.90/2.01 % (1371720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/2.01 % (1371720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/2.01 % (1371720)CaDiCaL version: 2.1.3
% 6.90/2.01 % (1371720)Termination reason: Refutation not found, incomplete strategy
% 6.90/2.01 % (1371720)Time elapsed: 0.001 s
% 6.90/2.01 % (1371720)Peak memory usage: 88 MB
% 6.90/2.01 % (1371699)------------------------------
% 6.90/2.01 % (1371699)------------------------------
% 6.90/2.01 % (1371722)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1258143674:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.90/2.01 % (1371722)Refutation not found, incomplete strategy
% 6.90/2.01 % (1371722)------------------------------
% 6.90/2.01 % (1371722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/2.01 % (1371722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/2.01 % (1371722)CaDiCaL version: 2.1.3
% 6.90/2.01 % (1371722)Termination reason: Refutation not found, incomplete strategy
% 6.90/2.01 % (1371722)Time elapsed: 0.001 s
% 6.90/2.01 % (1371722)Peak memory usage: 88 MB
% 6.90/2.01 % (1371722)Instructions burned: 1 (million)
% 6.90/2.01 % (1371693)First to succeed.
% 6.90/2.01 % (1371693)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1371587"
% 6.90/2.01 % (1371725)lrs+10_64_to=lpo:sil=8000:random_seed=3969568745:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.90/2.01 % (1371721)------------------------------
% 6.90/2.01 % (1371721)------------------------------
% 6.90/2.01 % (1371720)------------------------------
% 6.90/2.01 % (1371720)------------------------------
% 6.90/2.01 % (1371722)------------------------------
% 6.90/2.01 % (1371722)------------------------------
% 6.90/2.01 % (1371725)Instruction limit reached!
% 6.90/2.01 % (1371725)------------------------------
% 6.90/2.01 % (1371725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/2.01 % (1371725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/2.02 % (1371725)CaDiCaL version: 2.1.3
% 6.90/2.02 % (1371725)Termination reason: Instruction limit
% 6.90/2.02 % (1371725)Termination phase: Saturation
% 6.90/2.02 % (1371725)Time elapsed: 0.080 s
% 6.90/2.02 % (1371725)Peak memory usage: 89 MB
% 6.90/2.02 % (1371725)Instructions burned: 126 (million)
% 6.90/2.02 % (1371729)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3104128865:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.90/2.02 % (1371728)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1129316627:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 6.90/2.02 % (1371694)Also succeeded, but the first one will report.
% 6.90/2.02 % (1371728)Also succeeded, but the first one will report.
% 6.90/2.02 % (1371729)Instruction limit reached!
% 6.90/2.02 % (1371729)------------------------------
% 6.90/2.02 % (1371729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/2.02 % (1371729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/2.02 % (1371729)CaDiCaL version: 2.1.3
% 6.90/2.02 % (1371729)Termination reason: Instruction limit
% 6.90/2.02 % (1371729)Termination phase: Saturation
% 6.90/2.02 % (1371729)Time elapsed: 0.076 s
% 6.90/2.02 % (1371729)Peak memory usage: 91 MB
% 6.90/2.02 % (1371729)Instructions burned: 157 (million)
% 6.90/2.02 % (1371730)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1670071204:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.90/2.02 % (1371693)Refutation found. Thanks to Tanya!
% 6.90/2.02 % SZS status Unsatisfiable for theBenchmark
% 6.90/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 6.90/2.02 % (1371693)------------------------------
% 6.90/2.02 % (1371693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/2.02 % (1371693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/2.02 % (1371693)CaDiCaL version: 2.1.3
% 6.90/2.02 % (1371693)Termination reason: Refutation
% 6.90/2.02 % (1371693)Time elapsed: 0.468 s
% 6.90/2.02 % (1371693)Peak memory usage: 129 MB
% 6.90/2.02 % (1371693)Instructions burned: 1051 (million)
% 6.90/2.02 % (1371693)------------------------------
% 6.90/2.02 % (1371693)------------------------------
% 6.90/2.02 % (1371587)Success in time 0.899 s
% 6.90/2.02 % Vampire exiting
%------------------------------------------------------------------------------