%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 10:13:15 AM UTC 2026
% Result : Unsatisfiable 1.71s 1.78s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 73 unt; 8 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_3) ).
fof(f21,axiom,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_4) ).
fof(f22,axiom,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_5) ).
fof(f23,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21x) ).
fof(f24,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f25,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f25]) ).
fof(f27,definition,
! [X0] : sF1(X0) = multiply(inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f28,plain,
! [X0] : multiply(inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
! [X0] : identity = sF1(X0),
inference(definition_folding,[],[f3,f28]) ).
fof(f30,definition,
sF2 = inverse(identity),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f31,plain,
inverse(identity) = sF2,
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
identity = sF2,
inference(definition_folding,[],[f18,f31]) ).
fof(f33,definition,
sF3 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f34,plain,
least_upper_bound(a,identity) = sF3,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF4 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f36,plain,
greatest_lower_bound(a,identity) = sF4,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF5 = inverse(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f38,plain,
inverse(sF4) = sF5,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF6 = multiply(sF3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f40,plain,
multiply(sF3,sF5) = sF6,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF7 = multiply(sF5,sF3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f42,plain,
multiply(sF5,sF3) = sF7,
inference(reorient_equations,[],[f41]) ).
fof(f43,plain,
sF6 != sF7,
inference(definition_folding,[],[f23,f42,f34,f38,f36,f40,f38,f36,f34]) ).
fof(f44,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f29,f28]) ).
fof(f45,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f26,f25]) ).
fof(f51,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0),
inference(superposition,[],[f15,f45]) ).
fof(f52,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f45]) ).
fof(f53,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0),
inference(superposition,[],[f16,f45]) ).
fof(f55,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f53,f5]) ).
fof(f56,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f51,f6]) ).
fof(f63,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f44]) ).
fof(f76,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f63,f45]) ).
fof(f266,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f44,f19]) ).
fof(f639,plain,
inverse(sF4) = least_upper_bound(inverse(a),inverse(identity)),
inference(superposition,[],[f21,f36]) ).
fof(f647,plain,
inverse(sF4) = least_upper_bound(inverse(identity),inverse(a)),
inference(forward_demodulation,[],[f639,f6]) ).
fof(f653,plain,
inverse(sF4) = least_upper_bound(sF2,inverse(a)),
inference(forward_demodulation,[],[f647,f31]) ).
fof(f657,plain,
inverse(sF4) = least_upper_bound(identity,inverse(a)),
inference(forward_demodulation,[],[f653,f32]) ).
fof(f661,plain,
sF5 = least_upper_bound(identity,inverse(a)),
inference(forward_demodulation,[],[f657,f38]) ).
fof(f744,plain,
inverse(sF3) = greatest_lower_bound(inverse(a),inverse(identity)),
inference(superposition,[],[f22,f34]) ).
fof(f757,plain,
inverse(sF3) = greatest_lower_bound(inverse(identity),inverse(a)),
inference(forward_demodulation,[],[f744,f5]) ).
fof(f772,plain,
inverse(sF3) = greatest_lower_bound(sF2,inverse(a)),
inference(forward_demodulation,[],[f757,f31]) ).
fof(f782,plain,
inverse(sF3) = greatest_lower_bound(identity,inverse(a)),
inference(forward_demodulation,[],[f772,f32]) ).
fof(f1486,plain,
! [X0] : multiply(sF4,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(superposition,[],[f55,f36]) ).
fof(f1752,plain,
! [X0] : multiply(sF3,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(superposition,[],[f56,f34]) ).
fof(f2074,plain,
greatest_lower_bound(inverse(a),identity) = multiply(sF4,inverse(a)),
inference(superposition,[],[f1486,f266]) ).
fof(f2099,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(sF4,inverse(a)),
inference(forward_demodulation,[],[f2074,f5]) ).
fof(f2105,plain,
inverse(sF3) = multiply(sF4,inverse(a)),
inference(forward_demodulation,[],[f2099,f782]) ).
fof(f2128,plain,
inverse(inverse(sF3)) = multiply(inverse(inverse(a)),inverse(sF4)),
inference(superposition,[],[f20,f2105]) ).
fof(f2139,plain,
inverse(inverse(sF3)) = multiply(inverse(inverse(a)),sF5),
inference(forward_demodulation,[],[f2128,f38]) ).
fof(f2147,plain,
inverse(inverse(sF3)) = multiply(a,sF5),
inference(forward_demodulation,[],[f2139,f19]) ).
fof(f2152,plain,
sF3 = multiply(a,sF5),
inference(forward_demodulation,[],[f2147,f19]) ).
fof(f2168,plain,
sF5 = multiply(inverse(a),sF3),
inference(superposition,[],[f76,f2152]) ).
fof(f2203,plain,
least_upper_bound(sF3,sF5) = multiply(least_upper_bound(identity,inverse(a)),sF3),
inference(superposition,[],[f52,f2168]) ).
fof(f2208,plain,
multiply(sF5,sF3) = least_upper_bound(sF3,sF5),
inference(forward_demodulation,[],[f2203,f661]) ).
fof(f2215,plain,
sF7 = least_upper_bound(sF3,sF5),
inference(forward_demodulation,[],[f2208,f42]) ).
fof(f3224,plain,
multiply(sF3,sF5) = least_upper_bound(sF5,sF3),
inference(superposition,[],[f1752,f2152]) ).
fof(f3262,plain,
multiply(sF3,sF5) = least_upper_bound(sF3,sF5),
inference(forward_demodulation,[],[f3224,f6]) ).
fof(f3272,plain,
multiply(sF3,sF5) = sF7,
inference(forward_demodulation,[],[f3262,f2215]) ).
fof(f3278,plain,
sF6 = sF7,
inference(forward_demodulation,[],[f3272,f40]) ).
fof(f3281,plain,
sF6 != sF6,
inference(superposition,[],[f43,f3278]) ).
fof(f3294,plain,
$false,
inference(trivial_inequality_removal,[],[f3281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n020.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 09:37:20 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.71/1.78 % (3138838)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.71/1.78 % (3138850)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=802641053:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.71/1.78 % (3138853)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3893928095:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.71/1.78 % (3138849)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=1544514130:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.71/1.78 % (3138855)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1909374018:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.71/1.78 % (3138852)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4036987457:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.71/1.78 % (3138851)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3765962669:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.71/1.78 % (3138854)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2968778878:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.71/1.78 % (3138853)First to succeed.
% 1.71/1.78 % (3138853)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3138838"
% 1.71/1.78 % (3138852)Instruction limit reached!
% 1.71/1.78 % (3138852)------------------------------
% 1.71/1.78 % (3138852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.71/1.78 % (3138852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/1.78 % (3138852)CaDiCaL version: 2.1.3
% 1.71/1.78 % (3138852)Termination reason: Instruction limit
% 1.71/1.78 % (3138852)Termination phase: Saturation
% 1.71/1.78 % (3138852)Time elapsed: 0.138 s
% 1.71/1.78 % (3138852)Peak memory usage: 88 MB
% 1.71/1.78 % (3138852)Instructions burned: 137 (million)
% 1.71/1.78 % (3138854)Instruction limit reached!
% 1.71/1.78 % (3138854)------------------------------
% 1.71/1.78 % (3138854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.71/1.78 % (3138854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/1.78 % (3138854)CaDiCaL version: 2.1.3
% 1.71/1.78 % (3138854)Termination reason: Instruction limit
% 1.71/1.78 % (3138854)Termination phase: Saturation
% 1.71/1.78 % (3138854)Time elapsed: 0.267 s
% 1.71/1.78 % (3138854)Peak memory usage: 90 MB
% 1.71/1.78 % (3138854)Instructions burned: 257 (million)
% 1.71/1.78 % (3138863)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4205599582:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 1.71/1.78 % (3138853)Refutation found. Thanks to Tanya!
% 1.71/1.78 % SZS status Unsatisfiable for theBenchmark
% 1.71/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.82/2.12 % (3138853)------------------------------
% 5.82/2.12 % (3138853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/2.12 % (3138853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/2.12 % (3138853)CaDiCaL version: 2.1.3
% 5.82/2.12 % (3138853)Termination reason: Refutation
% 5.82/2.12 % (3138853)Time elapsed: 0.094 s
% 5.82/2.12 % (3138853)Peak memory usage: 89 MB
% 5.82/2.12 % (3138853)Instructions burned: 95 (million)
% 5.82/2.12 % (3138853)------------------------------
% 5.82/2.12 % (3138853)------------------------------
% 5.82/2.12 % (3138838)Success in time 0.687 s
% 5.82/2.12 % Vampire exiting
%------------------------------------------------------------------------------