%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 10:14:00 AM UTC 2026
% Result : Unsatisfiable 14.93s 3.08s
% Output : Refutation 14.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 128 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(X1,multiply(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(X0,multiply(X2,X4)))))),multiply(multiply(X0,X5),inverse(multiply(X6,multiply(X1,X5))))))) = X6,
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X0,multiply(X4,X3))))),X0)))) = X4,
inference(superposition,[],[f1,f1]) ).
fof(f11,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X0,X4))))),X5)),X0)))) = X3,
inference(superposition,[],[f1,f4]) ).
fof(f22,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X3,multiply(X6,X8)))))) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X0,multiply(X5,X4))))),X0)),X5)))),
inference(superposition,[],[f4,f3]) ).
fof(f145,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))) = X3,
inference(superposition,[],[f11,f22]) ).
fof(f206,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(inverse(X0),multiply(X1,X4)))))),inverse(multiply(X5,X0)))))) = X5,
inference(superposition,[],[f1,f145]) ).
fof(f319,plain,
! [X0,X1,X4] : inverse(multiply(inverse(X1),multiply(X1,multiply(X0,inverse(multiply(X4,X0)))))) = X4,
inference(superposition,[],[f206,f145]) ).
fof(f382,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X0,X4)))),X0))),inverse(multiply(X5,X1)))))) = X5,
inference(superposition,[],[f206,f319]) ).
fof(f383,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X0,X3)))),X0))) = X1,
inference(superposition,[],[f145,f319]) ).
fof(f384,plain,
! [X2,X3,X0,X1] : inverse(X1) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X0,X3)))),X0)))),
inference(superposition,[],[f1,f319]) ).
fof(f416,plain,
! [X2,X1,X5] : inverse(multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(X5,X1)))))) = X5,
inference(forward_demodulation,[],[f382,f383]) ).
fof(f439,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X1),inverse(multiply(X0,X3)))),X0)))) = X3,
inference(superposition,[],[f1,f416]) ).
fof(f498,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(X0,multiply(X3,X5))))) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X1),X0)),X3)))),
inference(superposition,[],[f439,f1]) ).
fof(f698,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X4,X3)))),X4))),inverse(multiply(inverse(X5),X0))))) = X5,
inference(superposition,[],[f145,f383]) ).
fof(f715,plain,
! [X0,X1,X5] : multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(inverse(X5),X0))))) = X5,
inference(forward_demodulation,[],[f698,f383]) ).
fof(f1032,plain,
! [X2,X3,X0,X1] : inverse(multiply(X3,inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(inverse(X0),X2)),X3)))))) = X2,
inference(superposition,[],[f1,f498]) ).
fof(f1153,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(inverse(X3),X0)),X2))))),multiply(X5,multiply(multiply(inverse(X5),multiply(X0,X6)),X1)))))) = X6,
inference(superposition,[],[f1032,f1032]) ).
fof(f1166,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X0,X1)))))) = multiply(inverse(inverse(X2)),inverse(multiply(inverse(X0),inverse(X3)))),
inference(superposition,[],[f1032,f715]) ).
fof(f1185,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,multiply(X1,multiply(inverse(X1),X2)))),X0)) = X2,
inference(superposition,[],[f1032,f1]) ).
fof(f1242,plain,
! [X2,X3,X0,X6,X4,X5] : multiply(inverse(inverse(multiply(X2,inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(inverse(X3),X0)),X2))))))),inverse(multiply(inverse(multiply(inverse(X5),multiply(X0,X6))),inverse(X5)))) = X6,
inference(forward_demodulation,[],[f1153,f1166]) ).
fof(f1269,plain,
! [X0,X6,X5] : multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X5),multiply(X0,X6))),inverse(X5)))) = X6,
inference(forward_demodulation,[],[f1242,f1032]) ).
fof(f1342,plain,
! [X0,X1,X5] : multiply(inverse(X1),inverse(multiply(inverse(multiply(X0,multiply(X1,X5))),X0))) = X5,
inference(superposition,[],[f1269,f1032]) ).
fof(f1587,plain,
! [X2,X3,X0,X1] : multiply(multiply(inverse(X1),multiply(X2,inverse(multiply(X3,X2)))),X3) = multiply(inverse(X1),inverse(multiply(inverse(X0),X0))),
inference(superposition,[],[f1342,f384]) ).
fof(f3165,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(X4),X4)) = inverse(multiply(inverse(multiply(X3,multiply(X0,multiply(multiply(inverse(X0),multiply(X1,inverse(multiply(X2,X1)))),X2)))),X3)),
inference(superposition,[],[f1185,f1587]) ).
fof(f3229,plain,
! [X3,X4] : inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(X4),X4)),
inference(forward_demodulation,[],[f3165,f384]) ).
fof(f3517,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),X3) = multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(multiply(inverse(X0),X0)),X1))))),
inference(superposition,[],[f715,f3229]) ).
fof(f3534,plain,
! [X3,X0] : multiply(inverse(X0),X0) = multiply(inverse(X3),X3),
inference(forward_demodulation,[],[f3517,f715]) ).
fof(f3837,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f3534]) ).
fof(f3913,plain,
$false,
inference(forward_subsumption_resolution,[],[f3837,f3534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 % Computer : n014.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sun Sep 27 10:04:32 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 13.90/2.98 % (563246)Detected a unit-equality problem, will run specialized UEQ schedule.
% 13.90/2.98 % (563313)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1809248499:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 13.90/2.98 % (563312)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=3825567253:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 13.90/2.98 % (563317)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2600370511:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 13.90/2.98 % (563311)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=4075973543:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 13.90/2.98 % (563315)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2414516039:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 13.90/2.98 % (563320)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=563524702:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 13.90/2.98 % (563318)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2426031765:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 13.90/2.98 % (563315)Instruction limit reached!
% 13.90/2.98 % (563315)------------------------------
% 13.90/2.98 % (563315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/2.98 % (563315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/2.98 % (563315)CaDiCaL version: 2.1.3
% 13.90/2.98 % (563315)Termination reason: Instruction limit
% 13.90/2.98 % (563315)Termination phase: Saturation
% 13.90/2.98 % (563315)Time elapsed: 0.073 s
% 13.90/2.98 % (563315)Peak memory usage: 88 MB
% 13.90/2.98 % (563315)Instructions burned: 136 (million)
% 13.90/2.98 % (563317)Instruction limit reached!
% 13.90/2.98 % (563317)------------------------------
% 13.90/2.98 % (563317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/2.98 % (563317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/2.98 % (563317)CaDiCaL version: 2.1.3
% 13.90/2.98 % (563317)Termination reason: Instruction limit
% 13.90/2.98 % (563317)Termination phase: Saturation
% 13.90/2.98 % (563317)Time elapsed: 0.093 s
% 13.90/2.98 % (563317)Peak memory usage: 89 MB
% 13.90/2.98 % (563317)Instructions burned: 181 (million)
% 13.90/2.98 % (563318)Instruction limit reached!
% 13.90/2.98 % (563318)------------------------------
% 13.90/2.98 % (563318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/2.98 % (563318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/2.98 % (563318)CaDiCaL version: 2.1.3
% 13.90/2.98 % (563318)Termination reason: Instruction limit
% 13.90/2.98 % (563318)Termination phase: Saturation
% 13.90/2.98 % (563318)Time elapsed: 0.144 s
% 13.90/2.98 % (563318)Peak memory usage: 90 MB
% 13.90/2.98 % (563318)Instructions burned: 257 (million)
% 13.90/2.98 % (563339)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3400725797:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 13.90/2.98 % (563340)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4162544896:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 13.90/2.98 % (563347)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=64747542:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 13.90/2.98 % (563347)Instruction limit reached!
% 13.90/2.98 % (563347)------------------------------
% 13.90/2.98 % (563347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/2.98 % (563347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/2.98 % (563347)CaDiCaL version: 2.1.3
% 13.90/2.98 % (563347)Termination reason: Instruction limit
% 13.90/2.98 % (563347)Termination phase: Saturation
% 13.90/2.98 % (563347)Time elapsed: 0.127 s
% 13.90/2.98 % (563347)Peak memory usage: 91 MB
% 13.90/2.98 % (563347)Instructions burned: 215 (million)
% 14.93/3.08 % (563389)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=4193535402: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)
% 14.93/3.08 % (563320)Instruction limit reached!
% 14.93/3.08 % (563320)------------------------------
% 14.93/3.08 % (563320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.08 % (563320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.08 % (563320)CaDiCaL version: 2.1.3
% 14.93/3.08 % (563320)Termination reason: Instruction limit
% 14.93/3.08 % (563320)Termination phase: Saturation
% 14.93/3.08 % (563320)Time elapsed: 0.605 s
% 14.93/3.08 % (563320)Peak memory usage: 98 MB
% 14.93/3.08 % (563320)Instructions burned: 1188 (million)
% 14.93/3.08 % (563389)Instruction limit reached!
% 14.93/3.08 % (563389)------------------------------
% 14.93/3.08 % (563389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.08 % (563389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.08 % (563389)CaDiCaL version: 2.1.3
% 14.93/3.08 % (563389)Termination reason: Instruction limit
% 14.93/3.08 % (563389)Termination phase: Saturation
% 14.93/3.08 % (563389)Time elapsed: 0.169 s
% 14.93/3.08 % (563389)Peak memory usage: 93 MB
% 14.93/3.08 % (563389)Instructions burned: 318 (million)
% 14.93/3.08 % (563432)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=3544001017:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 14.93/3.08 % (563433)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2111759909:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 14.93/3.08 % (563339)Instruction limit reached!
% 14.93/3.08 % (563339)------------------------------
% 14.93/3.08 % (563339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.08 % (563339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.08 % (563339)CaDiCaL version: 2.1.3
% 14.93/3.08 % (563339)Termination reason: Instruction limit
% 14.93/3.08 % (563339)Termination phase: Saturation
% 14.93/3.08 % (563339)Time elapsed: 1.217 s
% 14.93/3.08 % (563339)Peak memory usage: 140 MB
% 14.93/3.08 % (563339)Instructions burned: 2051 (million)
% 14.93/3.08 % (563436)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3809625489:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2984 on theBenchmark for (2984ds/14534Mi)
% 14.93/3.08 % (563340)First to succeed.
% 14.93/3.08 % (563340)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-563246"
% 14.93/3.08 % (563312)Also succeeded, but the first one will report.
% 14.93/3.08 % (563340)Refutation found. Thanks to Tanya!
% 14.93/3.08 % SZS status Unsatisfiable for theBenchmark
% 14.93/3.08 % SZS output start Proof for theBenchmark
% See solution above
% 14.93/3.08 % (563340)------------------------------
% 14.93/3.08 % (563340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.93/3.08 % (563340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.93/3.08 % (563340)CaDiCaL version: 2.1.3
% 14.93/3.08 % (563340)Termination reason: Refutation
% 14.93/3.08 % (563340)Time elapsed: 1.411 s
% 14.93/3.08 % (563340)Peak memory usage: 145 MB
% 14.93/3.08 % (563340)Instructions burned: 2444 (million)
% 14.93/3.08 % (563340)------------------------------
% 14.93/3.08 % (563340)------------------------------
% 14.93/3.08 % (563246)Success in time 2.024 s
% 14.93/3.08 % Vampire exiting
%------------------------------------------------------------------------------