%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP500-1 : 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 10:17:58 AM UTC 2026
% Result : Unsatisfiable 1.41s 0.69s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 11 ( 3 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 : 128 ( 128 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(double_divide(X0,double_divide(X1,X2))),double_divide(X3,double_divide(X1,X3))))) = X2,
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(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))),
inference(definition_unfolding,[],[f4,f2,f2]) ).
fof(f6,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(double_divide(inverse(double_divide(X2,double_divide(X3,X0))),double_divide(X4,double_divide(X3,X4)))) = double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X0)),double_divide(X5,double_divide(inverse(X2),X5))))),
inference(superposition,[],[f1,f1]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X0)))),double_divide(X3,double_divide(X2,X3)))) = X0,
inference(superposition,[],[f6,f1]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X3),double_divide(inverse(X0),inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,double_divide(inverse(X3),X2)))))) = X1,
inference(superposition,[],[f1,f6]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X4] : double_divide(X2,X3) = double_divide(inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X0))))),inverse(double_divide(X0,double_divide(X4,double_divide(X3,X4))))),
inference(superposition,[],[f1,f22]) ).
fof(f53,plain,
! [X0,X6,X4,X5] : double_divide(X0,double_divide(inverse(X4),inverse(double_divide(inverse(double_divide(X4,X5)),double_divide(X6,double_divide(X0,X6)))))) = X5,
inference(superposition,[],[f24,f22]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] : inverse(double_divide(inverse(double_divide(X1,X0)),double_divide(X3,double_divide(X2,X3)))) = inverse(double_divide(inverse(double_divide(X1,X0)),double_divide(X4,double_divide(X2,X4)))),
inference(superposition,[],[f22,f53]) ).
fof(f186,plain,
! [X2,X3,X0,X1,X6,X4,X5] : double_divide(X5,double_divide(X3,X5)) = double_divide(inverse(X4),double_divide(inverse(inverse(double_divide(X0,X1))),inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,double_divide(X3,X2)))),double_divide(X6,double_divide(inverse(X4),X6)))))),
inference(superposition,[],[f24,f84]) ).
fof(f196,plain,
! [X2,X3,X5] : double_divide(X5,double_divide(X3,X5)) = double_divide(X2,double_divide(X3,X2)),
inference(forward_demodulation,[],[f186,f24]) ).
fof(f219,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X0,double_divide(X1,X0))),double_divide(X3,double_divide(X1,X3))))) = X2,
inference(superposition,[],[f1,f196]) ).
fof(f231,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(double_divide(X1,double_divide(X0,double_divide(inverse(X1),X0)))),double_divide(X3,double_divide(X2,X3)))) = X2,
inference(superposition,[],[f22,f196]) ).
fof(f692,plain,
! [X2,X3,X0,X1] : double_divide(X0,X1) = inverse(double_divide(X2,double_divide(X0,double_divide(inverse(X2),inverse(double_divide(X3,double_divide(X1,X3))))))),
inference(superposition,[],[f219,f40]) ).
fof(f1067,plain,
! [X3,X0,X1,X4] : inverse(double_divide(double_divide(inverse(double_divide(X0,double_divide(X1,X0))),X1),double_divide(X3,double_divide(X4,X3)))) = X4,
inference(superposition,[],[f231,f692]) ).
fof(f1149,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X0,double_divide(X1,X0))),X1) = inverse(double_divide(inverse(double_divide(X2,double_divide(X3,X2))),X3)),
inference(superposition,[],[f1067,f692]) ).
fof(f1684,plain,
! [X2,X3,X0,X1,X4,X5] : double_divide(inverse(inverse(double_divide(X2,double_divide(double_divide(X3,X4),X2)))),inverse(double_divide(double_divide(inverse(double_divide(X0,double_divide(X1,X0))),X1),double_divide(X5,double_divide(X3,X5))))) = X4,
inference(superposition,[],[f1,f1149]) ).
fof(f1689,plain,
! [X2,X3,X0,X1,X4,X5] : double_divide(X2,double_divide(inverse(inverse(double_divide(X3,double_divide(X4,X3)))),inverse(double_divide(double_divide(inverse(double_divide(X0,double_divide(X1,X0))),X1),double_divide(X5,double_divide(X2,X5)))))) = X4,
inference(superposition,[],[f53,f1149]) ).
fof(f1708,plain,
! [X2,X3,X4] : double_divide(X2,double_divide(inverse(inverse(double_divide(X3,double_divide(X4,X3)))),X2)) = X4,
inference(forward_demodulation,[],[f1689,f1067]) ).
fof(f1710,plain,
! [X2,X3,X4] : double_divide(inverse(inverse(double_divide(X2,double_divide(double_divide(X3,X4),X2)))),X3) = X4,
inference(forward_demodulation,[],[f1684,f1067]) ).
fof(f1748,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X0)),double_divide(X2,double_divide(inverse(inverse(double_divide(X3,double_divide(X4,X3)))),X2))))),X0) = X4,
inference(superposition,[],[f1708,f53]) ).
fof(f1784,plain,
! [X3,X0,X1,X4] : double_divide(inverse(X1),inverse(double_divide(inverse(X0),double_divide(X4,double_divide(inverse(inverse(double_divide(X3,double_divide(X0,X3)))),X4))))) = X1,
inference(superposition,[],[f219,f1708]) ).
fof(f1852,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(double_divide(inverse(X0),X0))) = X1,
inference(forward_demodulation,[],[f1784,f1708]) ).
fof(f1856,plain,
! [X0,X1,X4] : double_divide(double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X0)),X4))),X0) = X4,
inference(forward_demodulation,[],[f1748,f1708]) ).
fof(f1889,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(inverse(double_divide(inverse(X0),X0)))) = X1,
inference(superposition,[],[f1852,f1852]) ).
fof(f1890,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(double_divide(X0,inverse(X0)))) = X1,
inference(superposition,[],[f1852,f40]) ).
fof(f2000,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(inverse(double_divide(X0,inverse(X0))))) = X1,
inference(superposition,[],[f1852,f1890]) ).
fof(f2093,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(inverse(inverse(double_divide(X0,inverse(X0)))))) = X1,
inference(superposition,[],[f1889,f1890]) ).
fof(f2934,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(inverse(double_divide(X0,X1))),
inference(superposition,[],[f1856,f1890]) ).
fof(f2998,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f2934,f1]) ).
fof(f3042,plain,
! [X0,X1] : double_divide(inverse(X1),double_divide(inverse(X0),X0)) = X1,
inference(superposition,[],[f1889,f2934]) ).
fof(f3045,plain,
! [X0,X1] : double_divide(inverse(X1),double_divide(X0,inverse(X0))) = X1,
inference(superposition,[],[f2000,f2934]) ).
fof(f3145,plain,
! [X0,X1] : inverse(X0) = double_divide(X0,inverse(inverse(double_divide(X1,inverse(X1))))),
inference(superposition,[],[f2000,f2998]) ).
fof(f3158,plain,
! [X0,X1] : inverse(X0) = double_divide(X0,double_divide(X1,inverse(X1))),
inference(forward_demodulation,[],[f3145,f2934]) ).
fof(f3574,plain,
! [X0,X1] : double_divide(X1,double_divide(X0,X1)) = X0,
inference(superposition,[],[f3042,f1708]) ).
fof(f4358,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X2)) = double_divide(inverse(inverse(double_divide(X1,double_divide(X0,X1)))),inverse(X0)),
inference(superposition,[],[f1710,f3045]) ).
fof(f4369,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X2)) = double_divide(double_divide(X1,double_divide(X0,X1)),inverse(X0)),
inference(forward_demodulation,[],[f4358,f2934]) ).
fof(f4483,plain,
! [X2,X0] : double_divide(X0,inverse(X0)) = double_divide(X2,inverse(X2)),
inference(forward_demodulation,[],[f4369,f3574]) ).
fof(f7031,plain,
! [X0] : a2 != inverse(double_divide(a2,inverse(double_divide(X0,inverse(X0))))),
inference(superposition,[],[f5,f4483]) ).
fof(f7451,plain,
! [X0] : a2 != inverse(double_divide(a2,inverse(inverse(double_divide(X0,inverse(X0)))))),
inference(superposition,[],[f7031,f2093]) ).
fof(f7462,plain,
! [X0] : a2 != inverse(double_divide(a2,double_divide(X0,inverse(X0)))),
inference(forward_demodulation,[],[f7451,f2934]) ).
fof(f7479,plain,
a2 != inverse(inverse(a2)),
inference(forward_demodulation,[],[f7462,f3158]) ).
fof(f7494,plain,
$false,
inference(forward_subsumption_resolution,[],[f7479,f2998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 10:11:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 1.41/0.69 % (2397802)Will run a generic schedule for satisfiability detection.
% 1.41/0.69 % (2397813)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4181495101:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.41/0.69 % (2397808)% WARNING: option uhcvi not known.
% 1.41/0.69 % (2397808)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4160791148:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.41/0.69 % (2397809)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=879588321:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.41/0.69 % (2397810)dis+10_1_sil=32000:sp=arity:random_seed=2241534790:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.41/0.69 % (2397811)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3054441763:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.41/0.69 % (2397812)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3450947861:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.41/0.69 % (2397807)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2783167070_3000 on theBenchmark for (3000ds/0Mi)
% 1.41/0.69 % TRYING [1]
% 1.41/0.69 % TRYING [2]
% 1.41/0.69 % TRYING [3]
% 1.41/0.69 % TRYING [4]
% 1.41/0.69 % (2397813)Instruction limit reached!
% 1.41/0.69 % (2397813)------------------------------
% 1.41/0.69 % (2397813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397813)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397813)Termination reason: Instruction limit
% 1.41/0.69 % (2397813)Termination phase: Saturation
% 1.41/0.69 % (2397813)Time elapsed: 0.054 s
% 1.41/0.69 % (2397813)Peak memory usage: 13 MB
% 1.41/0.69 % (2397813)Instructions burned: 159 (million)
% 1.41/0.69 % (2397810)Instruction limit reached!
% 1.41/0.69 % (2397810)------------------------------
% 1.41/0.69 % (2397810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397810)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397810)Termination reason: Instruction limit
% 1.41/0.69 % (2397810)Termination phase: Saturation
% 1.41/0.69 % (2397810)Time elapsed: 0.057 s
% 1.41/0.69 % (2397810)Peak memory usage: 12 MB
% 1.41/0.69 % (2397810)Instructions burned: 103 (million)
% 1.41/0.69 % (2397823)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3142003767:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.41/0.69 % TRYING [1]
% 1.41/0.69 % (2397811)Instruction limit reached!
% 1.41/0.69 % (2397811)------------------------------
% 1.41/0.69 % (2397811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397811)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397811)Termination reason: Instruction limit
% 1.41/0.69 % (2397811)Termination phase: Saturation
% 1.41/0.69 % (2397811)Time elapsed: 0.068 s
% 1.41/0.69 % (2397811)Peak memory usage: 12 MB
% 1.41/0.69 % (2397811)Instructions burned: 116 (million)
% 1.41/0.69 % TRYING [2]
% 1.41/0.69 % TRYING [3]
% 1.41/0.69 % (2397828)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2786684625:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.41/0.69 % (2397812)Instruction limit reached!
% 1.41/0.69 % (2397812)------------------------------
% 1.41/0.69 % (2397812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397812)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397812)Termination reason: Instruction limit
% 1.41/0.69 % (2397812)Termination phase: Saturation
% 1.41/0.69 % (2397812)Time elapsed: 0.076 s
% 1.41/0.69 % (2397812)Peak memory usage: 13 MB
% 1.41/0.69 % (2397812)Instructions burned: 131 (million)
% 1.41/0.69 % TRYING [4]
% 1.41/0.69 % (2397834)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2369181336:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.41/0.69 % (2397840)ott-21_1_sil=16000:fs=off:random_seed=1127642200:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.41/0.69 % (2397828)Instruction limit reached!
% 1.41/0.69 % (2397828)------------------------------
% 1.41/0.69 % (2397828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397828)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397828)Termination reason: Instruction limit
% 1.41/0.69 % (2397828)Termination phase: Saturation
% 1.41/0.69 % (2397828)Time elapsed: 0.079 s
% 1.41/0.69 % (2397828)Peak memory usage: 13 MB
% 1.41/0.69 % (2397828)Instructions burned: 132 (million)
% 1.41/0.69 % (2397875)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=128562326:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.41/0.69 % (2397840)Instruction limit reached!
% 1.41/0.69 % (2397840)------------------------------
% 1.41/0.69 % (2397840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397840)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397840)Termination reason: Instruction limit
% 1.41/0.69 % (2397840)Termination phase: Saturation
% 1.41/0.69 % (2397840)Time elapsed: 0.088 s
% 1.41/0.69 % (2397840)Peak memory usage: 12 MB
% 1.41/0.69 % (2397840)Instructions burned: 182 (million)
% 1.41/0.69 % (2397891)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4000093542:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.41/0.69 % TRYING [1]
% 1.41/0.69 % TRYING [2]
% 1.41/0.69 % TRYING [3]
% 1.41/0.69 % TRYING [4]
% 1.41/0.69 % (2397809) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2397802-2397809"...
% 1.41/0.69 % (2397809)...printing done.
% 1.41/0.69 % (2397809)Refutation found. Thanks to Tanya!
% 1.41/0.69 % SZS status Unsatisfiable for theBenchmark
% 1.41/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.69 % (2397809)------------------------------
% 1.41/0.69 % (2397809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.69 % (2397809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.69 % (2397809)CaDiCaL version: 2.1.3
% 1.41/0.69 % (2397809)Termination reason: Refutation
% 1.41/0.69 % (2397809)Time elapsed: 0.239 s
% 1.41/0.69 % (2397809)Peak memory usage: 16 MB
% 1.41/0.69 % (2397809)Instructions burned: 489 (million)
% 1.41/0.69 % (2397802)Success in time 0.265 s
% 1.41/0.69 % Vampire exiting
%------------------------------------------------------------------------------