%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP612-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:18:13 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f4,plain,
inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
inference(definition_unfolding,[],[f3,f2,f2]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : double_divide(X1,X2) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(inverse(double_divide(inverse(double_divide(X1,X0)),X2)),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f6,plain,
! [X2,X0,X1] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X0)),double_divide(X1,X2)))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X2,X1)),double_divide(X2,X0)) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(X1,X3))),
inference(superposition,[],[f1,f6]) ).
fof(f41,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(X1,X2)),double_divide(X1,inverse(double_divide(X2,X0)))) = X0,
inference(superposition,[],[f9,f1]) ).
fof(f45,plain,
! [X2,X0,X1] : inverse(double_divide(X2,inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1))))) = X0,
inference(superposition,[],[f6,f9]) ).
fof(f85,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(X0),double_divide(X1,double_divide(X1,inverse(double_divide(X2,X0)))))) = X2,
inference(superposition,[],[f1,f41]) ).
fof(f183,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(X2,double_divide(inverse(double_divide(X1,X2)),X0)))) = X0,
inference(superposition,[],[f5,f6]) ).
fof(f215,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(inverse(double_divide(X1,inverse(X2))),inverse(double_divide(X0,X2))),
inference(superposition,[],[f183,f85]) ).
fof(f298,plain,
! [X2,X0,X1] : inverse(double_divide(X1,X2)) = double_divide(X0,inverse(double_divide(inverse(X2),double_divide(X0,X1)))),
inference(superposition,[],[f183,f215]) ).
fof(f350,plain,
! [X0,X1] : inverse(inverse(double_divide(X0,double_divide(X1,X0)))) = X1,
inference(superposition,[],[f45,f298]) ).
fof(f391,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f350,f41]) ).
fof(f407,plain,
! [X0,X1] : double_divide(X1,double_divide(X0,X1)) = X0,
inference(superposition,[],[f391,f350]) ).
fof(f422,plain,
! [X0,X1] : double_divide(X0,inverse(inverse(double_divide(X0,X1)))) = X1,
inference(superposition,[],[f183,f407]) ).
fof(f464,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f422,f391]) ).
fof(f506,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[],[f464,f407]) ).
fof(f665,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(superposition,[],[f4,f506]) ).
fof(f666,plain,
$false,
inference(trivial_inequality_removal,[],[f665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP612-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:09:37 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
% 0.16/0.50 % (3283182)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (3283192)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=659538752:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (3283188)% WARNING: option uhcvi not known.
% 0.16/0.50 % (3283187)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4128103160_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (3283188)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4066256418:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (3283189)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4095269212:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (3283190)dis+10_1_sil=32000:sp=arity:random_seed=1223864800:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (3283191)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3051405701:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (3283193)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=579671419:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % TRYING [4]
% 0.16/0.50 % (3283189) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3283182-3283189"...
% 0.16/0.50 % (3283189)...printing done.
% 0.16/0.50 % (3283189)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (3283189)------------------------------
% 0.16/0.50 % (3283189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (3283189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (3283189)CaDiCaL version: 2.1.3
% 0.16/0.50 % (3283189)Termination reason: Refutation
% 0.16/0.50 % (3283189)Time elapsed: 0.029 s
% 0.16/0.50 % (3283189)Peak memory usage: 12 MB
% 0.16/0.50 % (3283189)Instructions burned: 51 (million)
% 0.16/0.50 % (3283182)Success in time 0.076 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------