%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL141-1 : 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 11:51:19 AM UTC 2026
% Result : Unsatisfiable 2.44s 1.26s
% Output : Refutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 42 unt; 5 def)
% Number of atoms : 109 ( 56 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 31 ~; 29 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 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,negated_conjecture,
implies(not(x),not(y)) != implies(y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
fof(f9,definition,
( spl0_1
<=> implies(not(x),not(y)) = implies(y,x) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f11,plain,
( implies(not(x),not(y)) != implies(y,x)
| spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f7,f9]) ).
fof(f16,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f33,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f39,plain,
! [X0,X1] : implies(implies(implies(X1,X0),implies(not(X0),not(X1))),implies(not(X0),not(X1))) = implies(truth,implies(X1,X0)),
inference(superposition,[],[f4,f6]) ).
fof(f40,plain,
! [X0,X1] : implies(X1,X0) = implies(implies(implies(X1,X0),implies(not(X0),not(X1))),implies(not(X0),not(X1))),
inference(forward_demodulation,[],[f39,f1]) ).
fof(f45,plain,
truth = implies(implies(not(truth),not(not(truth))),not(not(truth))),
inference(superposition,[],[f4,f33]) ).
fof(f48,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))),
inference(superposition,[],[f4,f33]) ).
fof(f51,plain,
! [X0] : implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))) = X0,
inference(forward_demodulation,[],[f48,f1]) ).
fof(f54,definition,
( spl0_2
<=> truth = implies(implies(not(truth),not(not(truth))),not(not(truth))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f56,plain,
( truth = implies(implies(not(truth),not(not(truth))),not(not(truth)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
spl0_2,
inference(avatar_split_clause,[],[f45,f54]) ).
fof(f68,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2))),
inference(superposition,[],[f3,f6]) ).
fof(f70,plain,
! [X0,X1] : truth = implies(implies(X1,truth),implies(X0,implies(X1,X0))),
inference(superposition,[],[f3,f1]) ).
fof(f77,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f93,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f77,f1]) ).
fof(f98,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2)),
inference(forward_demodulation,[],[f68,f1]) ).
fof(f107,plain,
( implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth)))
| ~ spl0_2 ),
inference(superposition,[],[f4,f56]) ).
fof(f108,plain,
( not(not(truth)) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f107,f1]) ).
fof(f118,definition,
( spl0_5
<=> not(not(truth)) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f120,plain,
( not(not(truth)) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f108,f54,f118]) ).
fof(f156,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f93,f16]) ).
fof(f164,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f93]) ).
fof(f167,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f192,plain,
! [X0] : truth = implies(X0,truth),
inference(backward_demodulation,[],[f156,f167]) ).
fof(f193,plain,
! [X0,X1] : truth = implies(truth,implies(X0,implies(X1,X0))),
inference(backward_demodulation,[],[f70,f192]) ).
fof(f205,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(forward_demodulation,[],[f193,f1]) ).
fof(f209,plain,
( not(not(truth)) = implies(truth,implies(not(truth),not(not(truth))))
| ~ spl0_5 ),
inference(backward_demodulation,[],[f120,f205]) ).
fof(f210,plain,
( not(not(truth)) = implies(not(truth),not(not(truth)))
| ~ spl0_5 ),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f213,definition,
( spl0_8
<=> not(not(truth)) = implies(not(truth),not(not(truth))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f215,plain,
( not(not(truth)) = implies(not(truth),not(not(truth)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,plain,
( spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f210,f118,f213]) ).
fof(f241,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(superposition,[],[f3,f205]) ).
fof(f250,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f241,f1]) ).
fof(f575,plain,
! [X0] : truth = implies(truth,implies(not(truth),X0)),
inference(superposition,[],[f250,f33]) ).
fof(f634,plain,
! [X0] : truth = implies(not(truth),X0),
inference(forward_demodulation,[],[f575,f1]) ).
fof(f655,plain,
( truth = not(not(truth))
| ~ spl0_8 ),
inference(backward_demodulation,[],[f215,f634]) ).
fof(f657,definition,
( spl0_11
<=> truth = not(not(truth)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f659,plain,
( truth = not(not(truth))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f660,plain,
( spl0_11
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f655,f213,f657]) ).
fof(f672,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f4,f634]) ).
fof(f691,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f672,f1]) ).
fof(f997,plain,
! [X0] : truth = implies(X0,implies(implies(not(not(truth)),not(X0)),not(truth))),
inference(superposition,[],[f98,f691]) ).
fof(f1076,plain,
( ! [X0] : truth = implies(X0,implies(implies(truth,not(X0)),not(truth)))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f997,f659]) ).
fof(f1101,plain,
( ! [X0] : truth = implies(X0,implies(not(X0),not(truth)))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1076,f1]) ).
fof(f1108,plain,
( ! [X0] : implies(truth,implies(not(X0),not(truth))) = X0
| ~ spl0_11 ),
inference(backward_demodulation,[],[f51,f1101]) ).
fof(f1110,plain,
( ! [X0] : implies(not(X0),not(truth)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1108,f1]) ).
fof(f1129,plain,
( ! [X0] : not(X0) = implies(X0,not(truth))
| ~ spl0_11 ),
inference(superposition,[],[f691,f1110]) ).
fof(f3128,plain,
( ! [X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,not(truth)),not(X0)))
| ~ spl0_11 ),
inference(superposition,[],[f3,f1129]) ).
fof(f3231,plain,
( ! [X0,X1] : truth = implies(implies(X0,X1),implies(not(X1),not(X0)))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f3128,f1129]) ).
fof(f3274,plain,
( ! [X0,X1] : implies(X1,X0) = implies(truth,implies(not(X0),not(X1)))
| ~ spl0_11 ),
inference(backward_demodulation,[],[f40,f3231]) ).
fof(f3300,plain,
( ! [X0,X1] : implies(X1,X0) = implies(not(X0),not(X1))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f3274,f1]) ).
fof(f3312,plain,
( $false
| spl0_1
| ~ spl0_11 ),
inference(backward_subsumption_resolution,[],[f11,f3300]) ).
fof(f3313,plain,
( spl0_1
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f3312]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f121]) ).
cnf(s12,plain,
( ~ spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f216]) ).
cnf(s15,plain,
( ~ spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f660]) ).
cnf(s16,plain,
( spl0_1
| ~ spl0_11 ),
inference(sat_conversion,[],[f3313]) ).
cnf(s18,plain,
spl0_5,
inference(rat,[],[s8,s2]) ).
cnf(s20,plain,
spl0_8,
inference(rat,[],[s12,s18]) ).
cnf(s21,plain,
spl0_11,
inference(rat,[],[s15,s20]) ).
cnf(s24,plain,
spl0_1,
inference(rat,[],[s16,s21]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s24]) ).
fof(f3319,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:24:24 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 2.44/1.26 % (1372575)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.44/1.26 % (1372597)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2174050168:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.44/1.26 % (1372594)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2530476601:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.44/1.26 % (1372593)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=2887873431:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.44/1.26 % (1372592)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=3794718560:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.44/1.26 % (1372595)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=531567292:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.44/1.26 % (1372597)First to succeed.
% 2.44/1.26 % (1372597)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1372575"
% 2.44/1.26 % (1372598)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2372211225:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.44/1.26 % (1372596)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2221306424:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.44/1.26 % (1372595)Also succeeded, but the first one will report.
% 2.44/1.26 % (1372598)Also succeeded, but the first one will report.
% 2.44/1.26 % (1372596)Instruction limit reached!
% 2.44/1.26 % (1372596)------------------------------
% 2.44/1.26 % (1372596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/1.26 % (1372596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/1.26 % (1372596)CaDiCaL version: 2.1.3
% 2.44/1.26 % (1372596)Termination reason: Instruction limit
% 2.44/1.26 % (1372596)Termination phase: Saturation
% 2.44/1.26 % (1372596)Time elapsed: 0.101 s
% 2.44/1.26 % (1372596)Peak memory usage: 89 MB
% 2.44/1.26 % (1372596)Instructions burned: 181 (million)
% 2.44/1.26 % (1372597)Refutation found. Thanks to Tanya!
% 2.44/1.26 % SZS status Unsatisfiable for theBenchmark
% 2.44/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.06/1.46 % (1372597)------------------------------
% 3.06/1.46 % (1372597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.46 % (1372597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.46 % (1372597)CaDiCaL version: 2.1.3
% 3.06/1.46 % (1372597)Termination reason: Refutation
% 3.06/1.46 % (1372597)Time elapsed: 0.049 s
% 3.06/1.46 % (1372597)Peak memory usage: 90 MB
% 3.06/1.46 % (1372597)Instructions burned: 137 (million)
% 3.06/1.46 % (1372597)------------------------------
% 3.06/1.46 % (1372597)------------------------------
% 3.06/1.46 % (1372575)Success in time 0.345 s
% 3.06/1.46 % Vampire exiting
%------------------------------------------------------------------------------