%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL138-1 : 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 : n001.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 7.98s 2.16s
% Output : Refutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 39 unt; 9 def)
% Number of atoms : 89 ( 40 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 65 ( 32 ~; 28 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 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(f7,negated_conjecture,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
fof(f8,definition,
sF0 = implies(y,z),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
implies(y,z) = sF0,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF1 = implies(x,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
implies(x,sF0) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
sF2 = implies(x,z),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
implies(x,z) = sF2,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF3 = implies(y,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
implies(y,sF2) = sF3,
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
sF1 != sF3,
inference(definition_folding,[],[f7,f15,f13,f11,f9]) ).
fof(f20,definition,
( spl4_1
<=> implies(y,sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f22,plain,
( implies(y,sF2) = sF3
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
spl4_1,
inference(avatar_split_clause,[],[f15,f20]) ).
fof(f25,definition,
( spl4_2
<=> implies(x,sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f27,plain,
( implies(x,sF0) = sF1
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
spl4_2,
inference(avatar_split_clause,[],[f11,f25]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : truth = implies(truth,implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),
inference(superposition,[],[f3,f3]) ).
fof(f37,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f46,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f37,f1]) ).
fof(f48,plain,
! [X2,X3,X0,X1] : truth = implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3)),
inference(forward_demodulation,[],[f32,f1]) ).
fof(f61,definition,
( spl4_3
<=> sF1 = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f63,plain,
( sF1 != sF3
| spl4_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f16,f61]) ).
fof(f66,definition,
( spl4_4
<=> implies(y,z) = sF0 ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f68,plain,
( implies(y,z) = sF0
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
spl4_4,
inference(avatar_split_clause,[],[f9,f66]) ).
fof(f74,definition,
( spl4_5
<=> implies(x,z) = sF2 ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f76,plain,
( implies(x,z) = sF2
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
spl4_5,
inference(avatar_split_clause,[],[f13,f74]) ).
fof(f111,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(superposition,[],[f3,f46]) ).
fof(f123,plain,
! [X2,X0,X1] : truth = implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f111,f1]) ).
fof(f383,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(superposition,[],[f48,f123]) ).
fof(f455,plain,
! [X2,X0,X1] : truth = implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f383,f1]) ).
fof(f569,plain,
! [X2,X0,X1] : implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2))) = implies(truth,implies(X0,implies(X1,X2))),
inference(superposition,[],[f4,f455]) ).
fof(f587,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2))),
inference(forward_demodulation,[],[f569,f1]) ).
fof(f616,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(truth,implies(X1,implies(X0,X2))),
inference(forward_demodulation,[],[f587,f455]) ).
fof(f624,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[],[f616,f1]) ).
fof(f674,plain,
( ! [X0] : implies(X0,sF2) = implies(x,implies(X0,z))
| ~ spl4_5 ),
inference(superposition,[],[f624,f76]) ).
fof(f3732,plain,
( implies(x,sF0) = implies(y,sF2)
| ~ spl4_4
| ~ spl4_5 ),
inference(superposition,[],[f674,f68]) ).
fof(f3803,plain,
( implies(x,sF0) = sF3
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f3732,f22]) ).
fof(f3831,plain,
( sF1 = sF3
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f3803,f27]) ).
fof(f3839,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f3831,f63]) ).
fof(f3840,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f3839]) ).
cnf(s1,plain,
spl4_1,
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl4_3,
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f3840]) ).
cnf(s9,plain,
~ spl4_1,
inference(rat,[],[s8,s5,s4,s3,s2]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9]) ).
fof(f3841,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:29:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 5.60/1.90 % (3711409)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.60/1.90 % (3711515)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=1245764542:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.60/1.90 % (3711521)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3525974002:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.60/1.90 % (3711520)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1921642150:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.60/1.90 % (3711518)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1908136811:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.60/1.90 % (3711517)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3432076208:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.60/1.90 % (3711516)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=1557575097:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.60/1.90 % (3711519)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2038040893:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.60/1.90 % (3711518)Instruction limit reached!
% 5.60/1.90 % (3711518)------------------------------
% 5.60/1.90 % (3711518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.90 % (3711518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.90 % (3711518)CaDiCaL version: 2.1.3
% 5.60/1.90 % (3711518)Termination reason: Instruction limit
% 5.60/1.90 % (3711518)Termination phase: Saturation
% 5.60/1.90 % (3711518)Time elapsed: 0.083 s
% 5.60/1.90 % (3711518)Peak memory usage: 88 MB
% 5.60/1.90 % (3711518)Instructions burned: 137 (million)
% 5.60/1.90 % (3711519)Instruction limit reached!
% 5.60/1.90 % (3711519)------------------------------
% 5.60/1.90 % (3711519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.90 % (3711519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.90 % (3711519)CaDiCaL version: 2.1.3
% 5.60/1.90 % (3711519)Termination reason: Instruction limit
% 5.60/1.90 % (3711519)Termination phase: Saturation
% 5.60/1.90 % (3711519)Time elapsed: 0.101 s
% 5.60/1.90 % (3711519)Peak memory usage: 89 MB
% 5.60/1.90 % (3711519)Instructions burned: 182 (million)
% 5.60/1.90 % (3711542)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1963117398:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.60/1.90 % (3711520)Instruction limit reached!
% 5.60/1.90 % (3711520)------------------------------
% 5.60/1.90 % (3711520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.90 % (3711520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.90 % (3711520)CaDiCaL version: 2.1.3
% 5.60/1.90 % (3711520)Termination reason: Instruction limit
% 5.60/1.90 % (3711520)Termination phase: Saturation
% 5.60/1.90 % (3711520)Time elapsed: 0.244 s
% 5.60/1.90 % (3711520)Peak memory usage: 90 MB
% 5.60/1.90 % (3711520)Instructions burned: 258 (million)
% 5.60/1.90 % (3711543)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3784568445:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.60/1.90 % (3711545)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1351266408:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 5.60/1.90 % (3711545)Instruction limit reached!
% 5.60/1.90 % (3711545)------------------------------
% 5.60/1.90 % (3711545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.90 % (3711545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.90 % (3711545)CaDiCaL version: 2.1.3
% 5.60/1.90 % (3711545)Termination reason: Instruction limit
% 5.60/1.90 % (3711545)Termination phase: Saturation
% 5.60/1.90 % (3711545)Time elapsed: 0.053 s
% 7.98/2.16 % (3711545)Peak memory usage: 88 MB
% 7.98/2.16 % (3711545)Instructions burned: 215 (million)
% 7.98/2.16 % (3711548)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1146634558:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 7.98/2.16 % (3711515)First to succeed.
% 7.98/2.16 % (3711515)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3711409"
% 7.98/2.16 % (3711516)Also succeeded, but the first one will report.
% 7.98/2.16 % (3711521)Also succeeded, but the first one will report.
% 7.98/2.16 % (3711548)Instruction limit reached!
% 7.98/2.16 % (3711548)------------------------------
% 7.98/2.16 % (3711548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/2.16 % (3711548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/2.16 % (3711548)CaDiCaL version: 2.1.3
% 7.98/2.16 % (3711548)Termination reason: Instruction limit
% 7.98/2.16 % (3711548)Termination phase: Saturation
% 7.98/2.16 % (3711548)Time elapsed: 0.095 s
% 7.98/2.16 % (3711548)Peak memory usage: 92 MB
% 7.98/2.16 % (3711548)Instructions burned: 318 (million)
% 7.98/2.16 % (3711515)Refutation found. Thanks to Tanya!
% 7.98/2.16 % SZS status Unsatisfiable for theBenchmark
% 7.98/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 7.98/2.16 % (3711515)------------------------------
% 7.98/2.16 % (3711515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.98/2.16 % (3711515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.98/2.16 % (3711515)CaDiCaL version: 2.1.3
% 7.98/2.16 % (3711515)Termination reason: Refutation
% 7.98/2.16 % (3711515)Time elapsed: 0.620 s
% 7.98/2.16 % (3711515)Peak memory usage: 132 MB
% 7.98/2.16 % (3711515)Instructions burned: 1313 (million)
% 7.98/2.16 % (3711515)------------------------------
% 7.98/2.16 % (3711515)------------------------------
% 7.98/2.16 % (3711409)Success in time 1.036 s
% 7.98/2.16 % Vampire exiting
%------------------------------------------------------------------------------