%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP434-1 : 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 : n005.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 10:13:59 AM UTC 2026
% Result : Unsatisfiable 1.48s 1.63s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 75 unt; 10 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 121 ( 121 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = multiply(multiply(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = inverse(sF0(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
! [X2,X0,X1] : inverse(sF0(X0,X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = multiply(sF1(X0,X1,X2),X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(sF1(X0,X1,X2),X0) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = multiply(sF2(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : multiply(sF2(X0,X1,X2),X1) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X3] : sF4(X3) = multiply(X3,inverse(X3)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f13,plain,
! [X3] : multiply(X3,inverse(X3)) = sF4(X3),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X3,X0,X1] : sF5(X0,X1,X2,X3) = multiply(sF3(X0,X1,X2),sF4(X3)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : multiply(sF3(X0,X1,X2),sF4(X3)) = sF5(X0,X1,X2,X3),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X2,X3,X0,X1] : sF6(X0,X1,X2,X3) = inverse(sF5(X0,X1,X2,X3)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : inverse(sF5(X0,X1,X2,X3)) = sF6(X0,X1,X2,X3),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X2,X3,X0,X1] : sF6(X0,X1,X2,X3) = X2,
inference(definition_folding,[],[f1,f17,f15,f13,f11,f9,f7,f5]) ).
fof(f19,definition,
sF7 = inverse(b2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
inverse(b2) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF8 = multiply(sF7,b2),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f22,plain,
multiply(sF7,b2) = sF8,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF9 = multiply(sF8,a2),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f24,plain,
multiply(sF8,a2) = sF9,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
a2 != sF9,
inference(definition_folding,[],[f3,f24,f22,f20]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : inverse(sF5(X0,X1,X2,X3)) = X2,
inference(forward_demodulation,[],[f18,f17]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : inverse(multiply(sF3(X0,X1,X2),sF4(X3))) = X2,
inference(forward_demodulation,[],[f26,f15]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : inverse(multiply(sF3(X0,X1,X2),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f27,f13]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(sF2(X0,X1,X2),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f28,f11]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(sF1(X0,X1,X2),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f29,f9]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(sF0(X0,X1,X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f30,f7]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f31,f5]) ).
fof(f34,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(sF8,X0)),sF7),b2),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[],[f32,f22]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X4,inverse(X4)))),
inference(superposition,[],[f32,f32]) ).
fof(f36,plain,
! [X2,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(b2,sF7))) = X2,
inference(superposition,[],[f32,f20]) ).
fof(f46,plain,
! [X0] : a2 = inverse(multiply(multiply(multiply(inverse(sF9),sF7),b2),multiply(X0,inverse(X0)))),
inference(superposition,[],[f34,f24]) ).
fof(f55,plain,
a2 = inverse(multiply(multiply(multiply(inverse(sF9),sF7),b2),multiply(b2,sF7))),
inference(superposition,[],[f46,f20]) ).
fof(f84,plain,
! [X0] : multiply(X0,inverse(X0)) = inverse(multiply(multiply(multiply(a2,multiply(inverse(sF9),sF7)),b2),multiply(b2,sF7))),
inference(superposition,[],[f36,f46]) ).
fof(f85,plain,
multiply(b2,sF7) = inverse(multiply(multiply(multiply(a2,multiply(inverse(sF9),sF7)),b2),multiply(b2,sF7))),
inference(superposition,[],[f36,f55]) ).
fof(f97,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(b2,sF7),
inference(forward_demodulation,[],[f84,f85]) ).
fof(f111,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(b2,sF7),X1)),X0),inverse(X0)),multiply(b2,sF7))) = X1,
inference(superposition,[],[f36,f97]) ).
fof(f113,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = inverse(multiply(multiply(multiply(inverse(multiply(b2,sF7)),X0),X1),multiply(b2,sF7))),
inference(superposition,[],[f36,f97]) ).
fof(f149,plain,
! [X2,X3,X0,X1] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b2,sF7))),
inference(forward_demodulation,[],[f35,f97]) ).
fof(f150,plain,
! [X2,X0,X1] : multiply(b2,sF7) = inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b2,sF7))),
inference(forward_demodulation,[],[f149,f97]) ).
fof(f258,plain,
! [X0,X1] : multiply(b2,sF7) = inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(b2,sF7)))),X0),X1)),
inference(superposition,[],[f150,f113]) ).
fof(f273,plain,
! [X0] : multiply(b2,sF7) = inverse(multiply(multiply(inverse(multiply(multiply(b2,sF7),inverse(multiply(b2,sF7)))),X0),inverse(X0))),
inference(superposition,[],[f258,f97]) ).
fof(f296,plain,
! [X0] : multiply(b2,sF7) = inverse(multiply(multiply(inverse(multiply(b2,sF7)),X0),inverse(X0))),
inference(forward_demodulation,[],[f273,f97]) ).
fof(f342,plain,
multiply(b2,sF7) = inverse(multiply(multiply(multiply(b2,sF7),inverse(multiply(b2,sF7))),multiply(b2,sF7))),
inference(superposition,[],[f258,f296]) ).
fof(f344,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(multiply(multiply(b2,sF7),inverse(multiply(b2,sF7))),X0),multiply(b2,sF7))),
inference(superposition,[],[f36,f296]) ).
fof(f353,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(multiply(b2,sF7),X0),multiply(b2,sF7))),
inference(forward_demodulation,[],[f344,f97]) ).
fof(f355,plain,
multiply(b2,sF7) = inverse(multiply(multiply(b2,sF7),multiply(b2,sF7))),
inference(forward_demodulation,[],[f342,f97]) ).
fof(f373,plain,
inverse(inverse(multiply(b2,sF7))) = inverse(multiply(multiply(b2,sF7),multiply(b2,sF7))),
inference(superposition,[],[f353,f97]) ).
fof(f387,plain,
multiply(b2,sF7) = inverse(inverse(multiply(b2,sF7))),
inference(forward_demodulation,[],[f373,f355]) ).
fof(f392,plain,
multiply(b2,sF7) = multiply(inverse(multiply(b2,sF7)),multiply(b2,sF7)),
inference(superposition,[],[f97,f387]) ).
fof(f395,plain,
multiply(b2,sF7) = inverse(multiply(multiply(b2,sF7),inverse(multiply(b2,sF7)))),
inference(superposition,[],[f296,f392]) ).
fof(f396,plain,
! [X0] : inverse(multiply(multiply(b2,sF7),X0)) = inverse(multiply(multiply(multiply(b2,sF7),X0),multiply(b2,sF7))),
inference(superposition,[],[f113,f392]) ).
fof(f403,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(b2,sF7),X0)),
inference(forward_demodulation,[],[f396,f353]) ).
fof(f404,plain,
multiply(b2,sF7) = inverse(multiply(b2,sF7)),
inference(forward_demodulation,[],[f395,f97]) ).
fof(f427,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(X0),b2),sF7),multiply(b2,sF7))) = X0,
inference(superposition,[],[f36,f403]) ).
fof(f599,plain,
! [X0] : multiply(multiply(b2,sF7),X0) = X0,
inference(superposition,[],[f427,f36]) ).
fof(f657,plain,
! [X0] : inverse(X0) = inverse(multiply(X0,multiply(b2,sF7))),
inference(superposition,[],[f353,f599]) ).
fof(f754,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(X0),b2),sF7),multiply(b2,sF7))) = multiply(X0,multiply(b2,sF7)),
inference(superposition,[],[f427,f657]) ).
fof(f757,plain,
! [X0] : multiply(X0,multiply(b2,sF7)) = X0,
inference(forward_demodulation,[],[f754,f427]) ).
fof(f845,plain,
! [X0] : inverse(multiply(multiply(inverse(multiply(multiply(b2,sF7),X0)),inverse(multiply(b2,sF7))),multiply(b2,sF7))) = X0,
inference(superposition,[],[f111,f757]) ).
fof(f861,plain,
! [X0] : inverse(multiply(inverse(multiply(multiply(b2,sF7),X0)),inverse(multiply(b2,sF7)))) = X0,
inference(forward_demodulation,[],[f845,f657]) ).
fof(f895,plain,
! [X0] : inverse(multiply(inverse(multiply(multiply(b2,sF7),X0)),multiply(b2,sF7))) = X0,
inference(forward_demodulation,[],[f861,f404]) ).
fof(f918,plain,
! [X0] : inverse(inverse(multiply(multiply(b2,sF7),X0))) = X0,
inference(forward_demodulation,[],[f895,f657]) ).
fof(f925,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f918,f403]) ).
fof(f926,plain,
b2 = inverse(sF7),
inference(superposition,[],[f925,f20]) ).
fof(f1022,plain,
multiply(sF7,b2) = multiply(b2,sF7),
inference(superposition,[],[f97,f926]) ).
fof(f1032,plain,
sF8 = multiply(b2,sF7),
inference(forward_demodulation,[],[f1022,f22]) ).
fof(f1069,plain,
! [X0] : multiply(sF8,X0) = X0,
inference(superposition,[],[f599,f1032]) ).
fof(f1100,plain,
a2 = sF9,
inference(superposition,[],[f1069,f24]) ).
fof(f1144,plain,
a2 != a2,
inference(superposition,[],[f25,f1100]) ).
fof(f1154,plain,
$false,
inference(trivial_inequality_removal,[],[f1144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 10:04:17 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 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
% 1.48/1.63 % (3759213)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.48/1.63 % (3759218)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=1692858147:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.48/1.63 % (3759219)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=3130062618:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.48/1.63 % (3759224)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4041474466:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.48/1.63 % (3759222)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1513519017:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.48/1.63 % (3759220)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1898893891:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.48/1.63 % (3759223)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2476117066:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.48/1.63 % (3759222)First to succeed.
% 1.48/1.63 % (3759221)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2664351926:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.48/1.63 % (3759222)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3759213"
% 1.48/1.63 % (3759221)Instruction limit reached!
% 1.48/1.63 % (3759221)------------------------------
% 1.48/1.63 % (3759221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.48/1.63 % (3759221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/1.63 % (3759221)CaDiCaL version: 2.1.3
% 1.48/1.63 % (3759221)Termination reason: Instruction limit
% 1.48/1.63 % (3759221)Termination phase: Saturation
% 1.48/1.63 % (3759221)Time elapsed: 0.099 s
% 1.48/1.63 % (3759221)Peak memory usage: 89 MB
% 1.48/1.63 % (3759221)Instructions burned: 137 (million)
% 1.48/1.63 % (3759223)Instruction limit reached!
% 1.48/1.63 % (3759223)------------------------------
% 1.48/1.63 % (3759223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.48/1.63 % (3759223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/1.63 % (3759223)CaDiCaL version: 2.1.3
% 1.48/1.63 % (3759223)Termination reason: Instruction limit
% 1.48/1.63 % (3759223)Termination phase: Saturation
% 1.48/1.63 % (3759223)Time elapsed: 0.141 s
% 1.48/1.63 % (3759223)Peak memory usage: 90 MB
% 1.48/1.63 % (3759223)Instructions burned: 257 (million)
% 1.48/1.63 % (3759232)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3943966429:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 1.48/1.63 % (3759233)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1521779006:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 1.48/1.63 % (3759222)Refutation found. Thanks to Tanya!
% 1.48/1.63 % SZS status Unsatisfiable for theBenchmark
% 1.48/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.82 % (3759222)------------------------------
% 3.97/1.82 % (3759222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.82 % (3759222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.82 % (3759222)CaDiCaL version: 2.1.3
% 3.97/1.82 % (3759222)Termination reason: Refutation
% 3.97/1.82 % (3759222)Time elapsed: 0.030 s
% 3.97/1.82 % (3759222)Peak memory usage: 88 MB
% 3.97/1.82 % (3759222)Instructions burned: 53 (million)
% 3.97/1.82 % (3759222)------------------------------
% 3.97/1.82 % (3759222)------------------------------
% 3.97/1.82 % (3759213)Success in time 0.423 s
% 3.97/1.82 % Vampire exiting
%------------------------------------------------------------------------------