%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 10:16:22 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
fof(f19,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f23,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f7,f4]) ).
fof(f24,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f19,f1]) ).
fof(f100,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,X1))) = multiply(inverse(X0),identity),
inference(superposition,[],[f24,f23]) ).
fof(f113,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f100,f5]) ).
fof(f196,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f24,f113]) ).
fof(f838,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(superposition,[],[f8,f196]) ).
fof(f861,plain,
$false,
inference(trivial_inequality_removal,[],[f838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.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 09:13:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 % (1753446)Will run a generic schedule for satisfiability detection.
% 0.19/0.49 % (1753455)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3125549495:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.49 % (1753452)% WARNING: option uhcvi not known.
% 0.19/0.49 % (1753455) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1753446-1753455"...
% 0.19/0.49 % (1753452)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1144653143:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.49 % (1753454)dis+10_1_sil=32000:sp=arity:random_seed=3179282838:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.49 % (1753451)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2083964543_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.49 % (1753453)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1784735191:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.49 % (1753455)...printing done.
% 0.19/0.49 % (1753457)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3521666947:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.49 % (1753456)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1392676529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.49 % (1753455)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (1753455)------------------------------
% 0.19/0.49 % (1753455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (1753455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (1753455)CaDiCaL version: 2.1.3
% 0.19/0.49 % (1753455)Termination reason: Refutation
% 0.19/0.49 % (1753455)Time elapsed: 0.013 s
% 0.19/0.49 % (1753455)Peak memory usage: 11 MB
% 0.19/0.49 % (1753455)Instructions burned: 22 (million)
% 0.19/0.49 % (1753446)Success in time 0.045 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------