%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP421-1 : 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 : n013.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 10:13:57 AM UTC 2026
% Result : Unsatisfiable 6.40s 1.86s
% Output : Refutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 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 : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2))) = X1,
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,X4] : multiply(inverse(multiply(X2,inverse(multiply(inverse(X0),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X2,X3)) = inverse(multiply(inverse(multiply(X1,inverse(multiply(X0,multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X1,X4))),
inference(superposition,[],[f1,f1]) ).
fof(f5,plain,
! [X2,X0,X1] : multiply(inverse(X2),inverse(multiply(inverse(X0),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))))) = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),
inference(superposition,[],[f1,f1]) ).
fof(f12,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,X2))),
inference(superposition,[],[f5,f5]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(multiply(X4,X1)),multiply(X4,X2)) = inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),multiply(inverse(X5),inverse(multiply(inverse(X5),X5))))))),multiply(X3,X5))),
inference(superposition,[],[f1,f12]) ).
fof(f65,plain,
! [X2,X0,X1,X4] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X4,X1)),multiply(X4,X2)),
inference(forward_demodulation,[],[f64,f1]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,multiply(X1,X2))),multiply(X4,X3)) = multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),X3)),
inference(superposition,[],[f65,f1]) ).
fof(f277,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X1,X2)) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f6004,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,multiply(X2,X3))),
inference(superposition,[],[f70,f277]) ).
fof(f7037,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f6004,f277]) ).
fof(f7841,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f7037]) ).
fof(f7983,plain,
$false,
inference(forward_subsumption_resolution,[],[f7841,f7037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:03:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 6.40/1.86 % (4170266)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.40/1.86 % (4170274)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2709158912:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.40/1.86 % (4170272)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=2840930348:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.40/1.86 % (4170271)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=757619242:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.40/1.86 % (4170276)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2543415586:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.40/1.86 % (4170277)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3061884008:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.40/1.86 % (4170273)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2146350229:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.40/1.86 % (4170275)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=788271677:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.40/1.86 % (4170274)Instruction limit reached!
% 6.40/1.86 % (4170274)------------------------------
% 6.40/1.86 % (4170274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.86 % (4170274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.86 % (4170274)CaDiCaL version: 2.1.3
% 6.40/1.86 % (4170274)Termination reason: Instruction limit
% 6.40/1.86 % (4170274)Termination phase: Saturation
% 6.40/1.86 % (4170274)Time elapsed: 0.043 s
% 6.40/1.86 % (4170274)Peak memory usage: 89 MB
% 6.40/1.86 % (4170274)Instructions burned: 139 (million)
% 6.40/1.86 % (4170285)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=819448994:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.40/1.86 % (4170275)Instruction limit reached!
% 6.40/1.86 % (4170275)------------------------------
% 6.40/1.86 % (4170275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.86 % (4170275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.86 % (4170275)CaDiCaL version: 2.1.3
% 6.40/1.86 % (4170275)Termination reason: Instruction limit
% 6.40/1.86 % (4170275)Termination phase: Saturation
% 6.40/1.86 % (4170275)Time elapsed: 0.096 s
% 6.40/1.86 % (4170275)Peak memory usage: 89 MB
% 6.40/1.86 % (4170275)Instructions burned: 182 (million)
% 6.40/1.86 % (4170276)Instruction limit reached!
% 6.40/1.86 % (4170276)------------------------------
% 6.40/1.86 % (4170276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.86 % (4170276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.86 % (4170276)CaDiCaL version: 2.1.3
% 6.40/1.86 % (4170276)Termination reason: Instruction limit
% 6.40/1.86 % (4170276)Termination phase: Saturation
% 6.40/1.86 % (4170276)Time elapsed: 0.153 s
% 6.40/1.86 % (4170276)Peak memory usage: 91 MB
% 6.40/1.86 % (4170276)Instructions burned: 258 (million)
% 6.40/1.86 % (4170287)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3834330615:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.40/1.86 % (4170288)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3825598777:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 6.40/1.86 % (4170288)Instruction limit reached!
% 6.40/1.86 % (4170288)------------------------------
% 6.40/1.86 % (4170288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.86 % (4170288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.86 % (4170288)CaDiCaL version: 2.1.3
% 6.40/1.86 % (4170288)Termination reason: Instruction limit
% 6.40/1.86 % (4170288)Termination phase: Saturation
% 6.40/1.86 % (4170288)Time elapsed: 0.126 s
% 6.40/1.86 % (4170288)Peak memory usage: 90 MB
% 6.40/1.86 % (4170288)Instructions burned: 216 (million)
% 6.40/1.86 % (4170277)First to succeed.
% 6.40/1.86 % (4170277)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4170266"
% 6.40/1.86 % (4170285)Also succeeded, but the first one will report.
% 6.40/1.86 % (4170291)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=725442873: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)
% 6.40/1.86 % (4170277)Refutation found. Thanks to Tanya!
% 6.40/1.86 % SZS status Unsatisfiable for theBenchmark
% 6.40/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 6.40/1.86 % (4170277)------------------------------
% 6.40/1.86 % (4170277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.86 % (4170277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.86 % (4170277)CaDiCaL version: 2.1.3
% 6.40/1.86 % (4170277)Termination reason: Refutation
% 6.40/1.86 % (4170277)Time elapsed: 0.422 s
% 6.40/1.86 % (4170277)Peak memory usage: 93 MB
% 6.40/1.86 % (4170277)Instructions burned: 830 (million)
% 6.40/1.86 % (4170277)------------------------------
% 6.40/1.86 % (4170277)------------------------------
% 6.40/1.86 % (4170266)Success in time 0.823 s
% 6.40/1.86 % Vampire exiting
%------------------------------------------------------------------------------