%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP597-1 : 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 10:14:57 AM UTC 2026
% Result : Unsatisfiable 3.00s 1.38s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 60 unt; 11 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f4,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(definition_unfolding,[],[f3,f2,f2]) ).
fof(f5,definition,
! [X2,X1] : sF0(X2,X1) = double_divide(inverse(X2),X1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X1] : double_divide(inverse(X2),X1) = sF0(X2,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X1] : sF1(X2,X1) = inverse(sF0(X2,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X1] : inverse(sF0(X2,X1)) = sF1(X2,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X2,X1) = double_divide(X0,sF1(X2,X1)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(X0,sF1(X2,X1)) = sF2(X0,X2,X1),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X0,X2,X1) = inverse(sF2(X0,X2,X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : inverse(sF2(X0,X2,X1)) = sF3(X0,X2,X1),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = double_divide(double_divide(X0,X1),sF3(X0,X2,X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),sF3(X0,X2,X1)) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : sF4(X0,X1,X2) = X2,
inference(definition_folding,[],[f1,f14,f12,f10,f8,f6]) ).
fof(f16,definition,
sF5 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
inverse(a1) = sF5,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF6 = double_divide(a1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
double_divide(a1,sF5) = sF6,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF7 = inverse(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
inverse(sF6) = sF7,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF8 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
inverse(b1) = sF8,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF9 = double_divide(b1,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f25,plain,
double_divide(b1,sF8) = sF9,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF10 = inverse(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f27,plain,
inverse(sF9) = sF10,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF7 != sF10,
inference(definition_folding,[],[f4,f27,f25,f23,f21,f19,f17]) ).
fof(f29,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),sF3(X0,X2,X1)) = X2,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f30,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(sF2(X0,X2,X1))) = X2,
inference(forward_demodulation,[],[f29,f12]) ).
fof(f31,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,sF1(X2,X1)))) = X2,
inference(forward_demodulation,[],[f30,f10]) ).
fof(f32,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(sF0(X2,X1))))) = X2,
inference(forward_demodulation,[],[f31,f8]) ).
fof(f33,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
inference(forward_demodulation,[],[f32,f6]) ).
fof(f35,plain,
! [X0] : double_divide(sF6,inverse(double_divide(a1,inverse(double_divide(inverse(X0),sF5))))) = X0,
inference(superposition,[],[f33,f19]) ).
fof(f36,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(X1,X2),inverse(double_divide(inverse(X3),inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))))))) = X3,
inference(superposition,[],[f33,f33]) ).
fof(f39,plain,
! [X0,X1] : sF6 = double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(sF7,X1))))),
inference(superposition,[],[f33,f21]) ).
fof(f40,plain,
! [X0,X1] : sF9 = double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(sF10,X1))))),
inference(superposition,[],[f33,f27]) ).
fof(f204,plain,
! [X0] : sF9 = double_divide(double_divide(double_divide(sF10,X0),inverse(double_divide(sF10,X0))),inverse(sF9)),
inference(superposition,[],[f40,f40]) ).
fof(f207,plain,
! [X0] : sF6 = double_divide(double_divide(double_divide(sF7,X0),inverse(double_divide(sF10,X0))),inverse(sF9)),
inference(superposition,[],[f39,f40]) ).
fof(f214,plain,
! [X0] : sF6 = double_divide(double_divide(double_divide(sF7,X0),inverse(double_divide(sF10,X0))),sF10),
inference(forward_demodulation,[],[f207,f27]) ).
fof(f217,plain,
! [X0] : sF9 = double_divide(double_divide(double_divide(sF10,X0),inverse(double_divide(sF10,X0))),sF10),
inference(forward_demodulation,[],[f204,f27]) ).
fof(f448,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(inverse(X3)),X2))))),inverse(X0)))) = X3,
inference(superposition,[],[f36,f36]) ).
fof(f501,plain,
! [X0] : sF9 = double_divide(double_divide(X0,inverse(X0)),sF10),
inference(superposition,[],[f217,f36]) ).
fof(f505,plain,
! [X3,X0] : double_divide(X0,inverse(double_divide(inverse(X3),inverse(X0)))) = X3,
inference(forward_demodulation,[],[f448,f33]) ).
fof(f609,plain,
! [X0] : sF6 = double_divide(X0,inverse(double_divide(sF7,inverse(X0)))),
inference(superposition,[],[f505,f21]) ).
fof(f610,plain,
! [X0] : sF9 = double_divide(X0,inverse(double_divide(sF10,inverse(X0)))),
inference(superposition,[],[f505,f27]) ).
fof(f611,plain,
! [X0] : double_divide(a1,inverse(double_divide(inverse(X0),sF5))) = X0,
inference(superposition,[],[f505,f17]) ).
fof(f681,plain,
sF9 = double_divide(double_divide(b1,sF8),sF10),
inference(superposition,[],[f501,f23]) ).
fof(f691,plain,
sF9 = double_divide(sF9,sF10),
inference(forward_demodulation,[],[f681,f25]) ).
fof(f990,plain,
sF6 = double_divide(sF6,inverse(double_divide(sF7,sF7))),
inference(superposition,[],[f609,f21]) ).
fof(f1154,plain,
sF9 = double_divide(sF6,inverse(double_divide(sF10,sF7))),
inference(superposition,[],[f610,f21]) ).
fof(f1337,plain,
! [X0] : double_divide(sF6,inverse(X0)) = X0,
inference(superposition,[],[f35,f611]) ).
fof(f1358,plain,
sF6 = double_divide(sF7,sF7),
inference(superposition,[],[f1337,f990]) ).
fof(f1445,plain,
sF6 = double_divide(double_divide(sF6,inverse(double_divide(sF10,sF7))),sF10),
inference(superposition,[],[f214,f1358]) ).
fof(f1459,plain,
sF6 = double_divide(sF9,sF10),
inference(forward_demodulation,[],[f1445,f1154]) ).
fof(f1468,plain,
sF6 = sF9,
inference(forward_demodulation,[],[f1459,f691]) ).
fof(f1472,plain,
inverse(sF6) = sF10,
inference(superposition,[],[f27,f1468]) ).
fof(f1502,plain,
sF7 = sF10,
inference(forward_demodulation,[],[f1472,f21]) ).
fof(f1504,plain,
sF7 != sF7,
inference(superposition,[],[f28,f1502]) ).
fof(f1536,plain,
$false,
inference(trivial_inequality_removal,[],[f1504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP597-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:07:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.00/1.38 % (4181404)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.00/1.38 % (4181433)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2682786478:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.00/1.38 % (4181431)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1071140693:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.00/1.38 % (4181432)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3307358700:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.00/1.38 % (4181435)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=578324458:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.00/1.38 % (4181434)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2716476889:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.00/1.38 % (4181430)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=511318207:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.00/1.38 % (4181429)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=3672245421:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.00/1.38 % (4181433)First to succeed.
% 3.00/1.38 % (4181433)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4181404"
% 3.00/1.38 % (4181432)Instruction limit reached!
% 3.00/1.38 % (4181432)------------------------------
% 3.00/1.38 % (4181432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.38 % (4181432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.38 % (4181432)CaDiCaL version: 2.1.3
% 3.00/1.38 % (4181432)Termination reason: Instruction limit
% 3.00/1.38 % (4181432)Termination phase: Saturation
% 3.00/1.38 % (4181432)Time elapsed: 0.080 s
% 3.00/1.38 % (4181432)Peak memory usage: 88 MB
% 3.00/1.38 % (4181432)Instructions burned: 137 (million)
% 3.00/1.38 % (4181435)Also succeeded, but the first one will report.
% 3.00/1.38 % (4181434)Also succeeded, but the first one will report.
% 3.00/1.38 % (4181433)Refutation found. Thanks to Tanya!
% 3.00/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.00/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/1.38 % (4181433)------------------------------
% 3.00/1.38 % (4181433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.38 % (4181433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.38 % (4181433)CaDiCaL version: 2.1.3
% 3.00/1.38 % (4181433)Termination reason: Refutation
% 3.00/1.38 % (4181433)Time elapsed: 0.025 s
% 3.00/1.38 % (4181433)Peak memory usage: 89 MB
% 3.00/1.38 % (4181433)Instructions burned: 82 (million)
% 3.00/1.38 % (4181433)------------------------------
% 3.00/1.38 % (4181433)------------------------------
% 3.00/1.38 % (4181404)Success in time 0.341 s
% 3.00/1.38 % Vampire exiting
%------------------------------------------------------------------------------