%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 11:51:13 AM UTC 2026
% Result : Unsatisfiable 14.28s 3.17s
% Output : Refutation 14.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f6,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f7,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f6]) ).
fof(f13,axiom,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
fof(f14,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(reorient_equations,[],[f13]) ).
fof(f19,axiom,
! [X2,X0,X1] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
fof(f22,axiom,
! [X0] : not(not(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_9) ).
fof(f23,axiom,
! [X0,X1] : implies(not(X0),not(X1)) = implies(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
fof(f24,plain,
! [X0,X1] : implies(X1,X0) = implies(not(X0),not(X1)),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
fof(f26,plain,
truth != implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
truth != implies(b,implies(implies(implies(a,b),implies(b,a)),a)),
inference(backward_demodulation,[],[f26,f19]) ).
fof(f29,plain,
! [X0,X1] : truth = implies(X1,implies(implies(not(X0),not(X1)),X0)),
inference(forward_demodulation,[],[f7,f19]) ).
fof(f30,plain,
truth != implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
inference(forward_demodulation,[],[f27,f19]) ).
fof(f31,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f29,f24]) ).
fof(f120,plain,
! [X0,X1] : implies(truth,implies(X1,X0)) = implies(implies(implies(X1,X0),X0),X0),
inference(superposition,[],[f5,f14]) ).
fof(f139,plain,
! [X0,X1] : implies(X1,X0) = implies(implies(implies(X1,X0),X0),X0),
inference(forward_demodulation,[],[f120,f2]) ).
fof(f144,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X0,not(X1)),
inference(superposition,[],[f24,f22]) ).
fof(f147,plain,
! [X0,X1] : implies(implies(not(X1),not(X0)),not(X0)) = implies(implies(X1,X0),not(X1)),
inference(superposition,[],[f5,f24]) ).
fof(f149,plain,
! [X2,X0,X1] : implies(X2,implies(X1,X0)) = implies(not(X0),implies(X2,not(X1))),
inference(superposition,[],[f19,f24]) ).
fof(f152,plain,
! [X0,X1] : implies(implies(X1,X0),not(X1)) = implies(implies(X0,X1),not(X0)),
inference(forward_demodulation,[],[f147,f24]) ).
fof(f153,plain,
! [X0,X1] : implies(implies(X1,X0),not(X1)) = implies(X0,not(implies(X0,X1))),
inference(forward_demodulation,[],[f152,f144]) ).
fof(f154,plain,
! [X0,X1] : implies(X0,not(implies(X0,X1))) = implies(X1,not(implies(X1,X0))),
inference(forward_demodulation,[],[f153,f144]) ).
fof(f400,plain,
! [X0,X1] : implies(X0,X1) = implies(implies(implies(X1,X0),X0),X1),
inference(superposition,[],[f139,f5]) ).
fof(f855,plain,
! [X2,X0,X1] : implies(not(X2),implies(X0,not(implies(X0,X1)))) = implies(X1,implies(implies(X1,X0),X2)),
inference(superposition,[],[f149,f154]) ).
fof(f877,plain,
! [X2,X0,X1] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(implies(X1,X0),X2)),
inference(forward_demodulation,[],[f855,f149]) ).
fof(f1021,plain,
! [X0,X1] : implies(implies(X1,X0),implies(X0,X1)) = implies(X0,implies(implies(X0,implies(X1,X0)),X1)),
inference(superposition,[],[f877,f400]) ).
fof(f1095,plain,
! [X0,X1] : implies(X0,implies(truth,X1)) = implies(implies(X1,X0),implies(X0,X1)),
inference(forward_demodulation,[],[f1021,f14]) ).
fof(f1126,plain,
! [X0,X1] : implies(X0,implies(truth,X1)) = implies(X0,implies(implies(X1,X0),X1)),
inference(forward_demodulation,[],[f1095,f19]) ).
fof(f1139,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(implies(X1,X0),X1)),
inference(forward_demodulation,[],[f1126,f2]) ).
fof(f1145,plain,
truth != implies(b,implies(implies(b,a),a)),
inference(backward_demodulation,[],[f30,f1139]) ).
fof(f1148,plain,
$false,
inference(forward_subsumption_resolution,[],[f1145,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 15:21:25 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 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
% 14.28/3.17 % (3089901)Detected a unit-equality problem, will run specialized UEQ schedule.
% 14.28/3.17 % (3089911)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2031896565:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 14.28/3.17 % (3089906)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=466269520:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 14.28/3.17 % (3089908)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3191748564:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 14.28/3.17 % (3089907)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=2791678166:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 14.28/3.17 % (3089910)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=692874035:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 14.28/3.17 % (3089909)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2138211141:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 14.28/3.17 % (3089912)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1557801612:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 14.28/3.17 % (3089911)Instruction limit reached!
% 14.28/3.17 % (3089911)------------------------------
% 14.28/3.17 % (3089911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089911)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089911)Termination reason: Instruction limit
% 14.28/3.17 % (3089911)Termination phase: Saturation
% 14.28/3.17 % (3089911)Time elapsed: 0.130 s
% 14.28/3.17 % (3089911)Peak memory usage: 90 MB
% 14.28/3.17 % (3089911)Instructions burned: 258 (million)
% 14.28/3.17 % (3089909)Instruction limit reached!
% 14.28/3.17 % (3089909)------------------------------
% 14.28/3.17 % (3089909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089909)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089909)Termination reason: Instruction limit
% 14.28/3.17 % (3089909)Termination phase: Saturation
% 14.28/3.17 % (3089909)Time elapsed: 0.133 s
% 14.28/3.17 % (3089909)Peak memory usage: 89 MB
% 14.28/3.17 % (3089909)Instructions burned: 136 (million)
% 14.28/3.17 % (3089910)Instruction limit reached!
% 14.28/3.17 % (3089910)------------------------------
% 14.28/3.17 % (3089910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089910)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089910)Termination reason: Instruction limit
% 14.28/3.17 % (3089910)Termination phase: Saturation
% 14.28/3.17 % (3089910)Time elapsed: 0.162 s
% 14.28/3.17 % (3089910)Peak memory usage: 89 MB
% 14.28/3.17 % (3089910)Instructions burned: 181 (million)
% 14.28/3.17 % (3089920)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3590927699:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 14.28/3.17 % (3089921)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1220430657:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 14.28/3.17 % (3089922)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=403356611:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 14.28/3.17 % (3089922)Instruction limit reached!
% 14.28/3.17 % (3089922)------------------------------
% 14.28/3.17 % (3089922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089922)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089922)Termination reason: Instruction limit
% 14.28/3.17 % (3089922)Termination phase: Saturation
% 14.28/3.17 % (3089922)Time elapsed: 0.196 s
% 14.28/3.17 % (3089922)Peak memory usage: 90 MB
% 14.28/3.17 % (3089922)Instructions burned: 215 (million)
% 14.28/3.17 % (3089926)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=4254699018:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 14.28/3.17 % (3089926)Instruction limit reached!
% 14.28/3.17 % (3089926)------------------------------
% 14.28/3.17 % (3089926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089926)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089926)Termination reason: Instruction limit
% 14.28/3.17 % (3089926)Termination phase: Saturation
% 14.28/3.17 % (3089926)Time elapsed: 0.180 s
% 14.28/3.17 % (3089926)Peak memory usage: 93 MB
% 14.28/3.17 % (3089926)Instructions burned: 319 (million)
% 14.28/3.17 % (3089912)Instruction limit reached!
% 14.28/3.17 % (3089912)------------------------------
% 14.28/3.17 % (3089912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089912)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089912)Termination reason: Instruction limit
% 14.28/3.17 % (3089912)Termination phase: Saturation
% 14.28/3.17 % (3089912)Time elapsed: 1.066 s
% 14.28/3.17 % (3089912)Peak memory usage: 101 MB
% 14.28/3.17 % (3089912)Instructions burned: 1188 (million)
% 14.28/3.17 % (3089920)First to succeed.
% 14.28/3.17 % (3089920)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3089901"
% 14.28/3.17 % (3089928)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1034484633:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 14.28/3.17 % (3089929)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2317639418:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 14.28/3.17 % (3089907)Also succeeded, but the first one will report.
% 14.28/3.17 % (3089920)Refutation found. Thanks to Tanya!
% 14.28/3.17 % SZS status Unsatisfiable for theBenchmark
% 14.28/3.17 % SZS output start Proof for theBenchmark
% See solution above
% 14.28/3.17 % (3089920)------------------------------
% 14.28/3.17 % (3089920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.28/3.17 % (3089920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.28/3.17 % (3089920)CaDiCaL version: 2.1.3
% 14.28/3.17 % (3089920)Termination reason: Refutation
% 14.28/3.17 % (3089920)Time elapsed: 0.870 s
% 14.28/3.17 % (3089920)Peak memory usage: 130 MB
% 14.28/3.17 % (3089920)Instructions burned: 1090 (million)
% 14.28/3.17 % (3089920)------------------------------
% 14.28/3.17 % (3089920)------------------------------
% 14.28/3.17 % (3089901)Success in time 1.912 s
% 14.28/3.17 % Vampire exiting
%------------------------------------------------------------------------------