%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL112-2 : 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 : n003.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 11:51:14 AM UTC 2026
% Result : Unsatisfiable 3.83s 1.63s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 41 unt; 5 def)
% Number of atoms : 108 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 33 ~; 30 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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,axiom,
! [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(not(x))) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_29) ).
fof(f8,plain,
truth != implies(x,not(not(x))),
inference(reorient_equations,[],[f7]) ).
fof(f10,definition,
( spl0_1
<=> truth = implies(x,not(not(x))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f12,plain,
( truth != implies(x,not(not(x)))
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f8,f10]) ).
fof(f17,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f34,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f46,plain,
truth = implies(implies(not(truth),not(not(truth))),not(not(truth))),
inference(superposition,[],[f4,f34]) ).
fof(f49,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))),
inference(superposition,[],[f4,f34]) ).
fof(f52,plain,
! [X0] : implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))) = X0,
inference(forward_demodulation,[],[f49,f1]) ).
fof(f55,definition,
( spl0_2
<=> truth = implies(implies(not(truth),not(not(truth))),not(not(truth))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f57,plain,
( truth = implies(implies(not(truth),not(not(truth))),not(not(truth)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
spl0_2,
inference(avatar_split_clause,[],[f46,f55]) ).
fof(f69,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(f71,plain,
! [X0,X1] : truth = implies(implies(X1,truth),implies(X0,implies(X1,X0))),
inference(superposition,[],[f3,f1]) ).
fof(f78,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f94,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f78,f1]) ).
fof(f99,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2)),
inference(forward_demodulation,[],[f69,f1]) ).
fof(f108,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,f57]) ).
fof(f109,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,[],[f108,f1]) ).
fof(f119,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(f121,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,[],[f119]) ).
fof(f122,plain,
( spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f109,f55,f119]) ).
fof(f157,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f94,f17]) ).
fof(f165,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f94]) ).
fof(f168,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f165,f1]) ).
fof(f193,plain,
! [X0] : truth = implies(X0,truth),
inference(backward_demodulation,[],[f157,f168]) ).
fof(f194,plain,
! [X0,X1] : truth = implies(truth,implies(X0,implies(X1,X0))),
inference(backward_demodulation,[],[f71,f193]) ).
fof(f206,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(forward_demodulation,[],[f194,f1]) ).
fof(f210,plain,
( not(not(truth)) = implies(truth,implies(not(truth),not(not(truth))))
| ~ spl0_5 ),
inference(backward_demodulation,[],[f121,f206]) ).
fof(f211,plain,
( not(not(truth)) = implies(not(truth),not(not(truth)))
| ~ spl0_5 ),
inference(forward_demodulation,[],[f210,f1]) ).
fof(f214,definition,
( spl0_8
<=> not(not(truth)) = implies(not(truth),not(not(truth))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f216,plain,
( not(not(truth)) = implies(not(truth),not(not(truth)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f211,f119,f214]) ).
fof(f242,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(superposition,[],[f3,f206]) ).
fof(f251,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f242,f1]) ).
fof(f576,plain,
! [X0] : truth = implies(truth,implies(not(truth),X0)),
inference(superposition,[],[f251,f34]) ).
fof(f635,plain,
! [X0] : truth = implies(not(truth),X0),
inference(forward_demodulation,[],[f576,f1]) ).
fof(f656,plain,
( truth = not(not(truth))
| ~ spl0_8 ),
inference(backward_demodulation,[],[f216,f635]) ).
fof(f658,definition,
( spl0_11
<=> truth = not(not(truth)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f660,plain,
( truth = not(not(truth))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f661,plain,
( spl0_11
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f656,f214,f658]) ).
fof(f673,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f4,f635]) ).
fof(f692,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f673,f1]) ).
fof(f998,plain,
! [X0] : truth = implies(X0,implies(implies(not(not(truth)),not(X0)),not(truth))),
inference(superposition,[],[f99,f692]) ).
fof(f1077,plain,
( ! [X0] : truth = implies(X0,implies(implies(truth,not(X0)),not(truth)))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f998,f660]) ).
fof(f1102,plain,
( ! [X0] : truth = implies(X0,implies(not(X0),not(truth)))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1077,f1]) ).
fof(f1109,plain,
( ! [X0] : implies(truth,implies(not(X0),not(truth))) = X0
| ~ spl0_11 ),
inference(backward_demodulation,[],[f52,f1102]) ).
fof(f1111,plain,
( ! [X0] : implies(not(X0),not(truth)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1109,f1]) ).
fof(f1130,plain,
( ! [X0] : not(X0) = implies(X0,not(truth))
| ~ spl0_11 ),
inference(superposition,[],[f692,f1111]) ).
fof(f1176,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl0_11 ),
inference(backward_demodulation,[],[f1111,f1130]) ).
fof(f1196,plain,
( truth != implies(x,x)
| spl0_1
| ~ spl0_11 ),
inference(backward_demodulation,[],[f12,f1176]) ).
fof(f1209,plain,
( truth != truth
| spl0_1
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1196,f168]) ).
fof(f1210,plain,
( $false
| spl0_1
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1209]) ).
fof(f1211,plain,
( spl0_1
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1210]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f58]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( ~ spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f217]) ).
cnf(s15,plain,
( ~ spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f661]) ).
cnf(s16,plain,
( spl0_1
| ~ spl0_11 ),
inference(sat_conversion,[],[f1211]) ).
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(f1216,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL112-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:24:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.83/1.63 % (696825)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.83/1.63 % (696855)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=459591043:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.83/1.63 % (696855)First to succeed.
% 3.83/1.63 % (696855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-696825"
% 3.83/1.63 % (696851)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=2924526198:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.83/1.63 % (696853)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1706674991:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.83/1.63 % (696850)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=2792618828:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.83/1.63 % (696852)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4116122865:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.83/1.63 % (696854)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=105156454:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.83/1.63 % (696856)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=93756928:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.83/1.63 % (696853)Also succeeded, but the first one will report.
% 3.83/1.63 % (696856)Also succeeded, but the first one will report.
% 3.83/1.63 % (696854)Also succeeded, but the first one will report.
% 3.83/1.63 % (696855)Refutation found. Thanks to Tanya!
% 3.83/1.63 % SZS status Unsatisfiable for theBenchmark
% 3.83/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.64 % (696855)------------------------------
% 3.83/1.64 % (696855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.64 % (696855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.64 % (696855)CaDiCaL version: 2.1.3
% 3.83/1.64 % (696855)Termination reason: Refutation
% 3.83/1.64 % (696855)Time elapsed: 0.032 s
% 3.83/1.64 % (696855)Peak memory usage: 89 MB
% 3.83/1.64 % (696855)Instructions burned: 53 (million)
% 3.83/1.64 % (696855)------------------------------
% 3.83/1.64 % (696855)------------------------------
% 3.83/1.64 % (696825)Success in time 0.434 s
% 3.83/1.64 % Vampire exiting
%------------------------------------------------------------------------------