%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 10:17:44 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : Refutation 0.17s
% 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 : 6 ( 4 avg)
% Maximal term depth : 10 ( 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 : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X2,inverse(multiply(X0,X3)))),multiply(X2,inverse(X3))) = multiply(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[],[f1,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,inverse(X2))),inverse(multiply(X3,multiply(inverse(X2),X2))))),X0),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f74,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[],[f3,f3]) ).
fof(f85,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X0,inverse(X2))) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f143,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X0))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(superposition,[],[f74,f85]) ).
fof(f208,plain,
! [X2,X0,X1,X6] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X0))) = multiply(inverse(multiply(X6,inverse(X2))),multiply(X6,inverse(X0))),
inference(superposition,[],[f143,f5]) ).
fof(f277,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(X3))) = multiply(inverse(X0),multiply(multiply(inverse(multiply(X4,inverse(multiply(X0,X2)))),multiply(X4,inverse(X2))),inverse(X3))),
inference(superposition,[],[f208,f1]) ).
fof(f374,plain,
! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))),
inference(superposition,[],[f277,f1]) ).
fof(f421,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f374,f374]) ).
fof(f554,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f421]) ).
fof(f591,plain,
$false,
inference(equality_resolution,[],[f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:08:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.51 % (2390720)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (2390729)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1196821040:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (2390726)% WARNING: option uhcvi not known.
% 0.17/0.51 % (2390725)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2188896991_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (2390726)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=23499920:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (2390727)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2132253323:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (2390728)dis+10_1_sil=32000:sp=arity:random_seed=2538796706:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (2390731)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3728292482:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % (2390730)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2032153605:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % (2390729)Instruction limit reached!
% 0.17/0.51 % (2390729)------------------------------
% 0.17/0.51 % (2390729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (2390729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (2390729)CaDiCaL version: 2.1.3
% 0.17/0.51 % (2390729)Termination reason: Instruction limit
% 0.17/0.51 % (2390729)Termination phase: Saturation
% 0.17/0.51 % (2390729)Time elapsed: 0.037 s
% 0.17/0.51 % (2390729)Peak memory usage: 12 MB
% 0.17/0.51 % (2390729)Instructions burned: 119 (million)
% 0.17/0.51 % (2390739)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3503536055:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % (2390731) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2390720-2390731"...
% 0.17/0.51 % (2390731)...printing done.
% 0.17/0.51 % (2390727) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2390720-2390727"...
% 0.17/0.51 % (2390731)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (2390731)------------------------------
% 0.17/0.51 % (2390731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (2390731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (2390731)CaDiCaL version: 2.1.3
% 0.17/0.51 % (2390731)Termination reason: Refutation
% 0.17/0.51 % (2390731)Time elapsed: 0.045 s
% 0.17/0.51 % (2390731)Peak memory usage: 12 MB
% 0.17/0.51 % (2390731)Instructions burned: 72 (million)
% 0.17/0.51 % (2390720)Success in time 0.087 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------