%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP175-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 10:13:11 AM UTC 2026
% Result : Unsatisfiable 1.57s 1.31s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 74 ( 74 unt; 7 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,axiom,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p06b_1) ).
fof(f18,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p06b) ).
fof(f20,plain,
identity != greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f22]) ).
fof(f24,definition,
! [X0] : sF1(X0) = multiply(inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : identity = sF1(X0),
inference(definition_folding,[],[f3,f25]) ).
fof(f27,definition,
sF2 = greatest_lower_bound(identity,b),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
greatest_lower_bound(identity,b) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
identity = sF2,
inference(definition_folding,[],[f18,f28]) ).
fof(f30,definition,
sF3 = inverse(a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f31,plain,
inverse(a) = sF3,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF4 = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f33,plain,
multiply(b,a) = sF4,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF5 = multiply(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
multiply(sF3,sF4) = sF5,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF6 = greatest_lower_bound(identity,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f37,plain,
greatest_lower_bound(identity,sF5) = sF6,
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
identity != sF6,
inference(definition_folding,[],[f20,f37,f35,f33,f31]) ).
fof(f39,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f26,f25]) ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f23,f22]) ).
fof(f47,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f40]) ).
fof(f49,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f40]) ).
fof(f56,plain,
identity = multiply(sF3,a),
inference(superposition,[],[f39,f31]) ).
fof(f57,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f39]) ).
fof(f58,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f39]) ).
fof(f70,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f57,f40]) ).
fof(f100,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f70,f39]) ).
fof(f102,plain,
a = multiply(inverse(b),sF4),
inference(superposition,[],[f70,f33]) ).
fof(f103,plain,
sF4 = multiply(inverse(sF3),sF5),
inference(superposition,[],[f70,f35]) ).
fof(f104,plain,
a = multiply(inverse(sF3),identity),
inference(superposition,[],[f70,f56]) ).
fof(f159,plain,
sF5 = multiply(inverse(inverse(sF3)),sF4),
inference(superposition,[],[f70,f103]) ).
fof(f173,plain,
identity = multiply(inverse(inverse(sF3)),a),
inference(superposition,[],[f70,f104]) ).
fof(f189,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f70,f100]) ).
fof(f319,plain,
a = multiply(inverse(inverse(inverse(sF3))),identity),
inference(superposition,[],[f70,f173]) ).
fof(f320,plain,
a = inverse(sF3),
inference(forward_demodulation,[],[f319,f100]) ).
fof(f437,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f70,f189]) ).
fof(f438,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f437,f100]) ).
fof(f446,plain,
! [X0] : greatest_lower_bound(X0,multiply(b,X0)) = multiply(sF2,X0),
inference(superposition,[],[f49,f28]) ).
fof(f516,plain,
! [X0] : multiply(identity,X0) = greatest_lower_bound(X0,multiply(b,X0)),
inference(forward_demodulation,[],[f446,f29]) ).
fof(f528,plain,
! [X0] : greatest_lower_bound(X0,multiply(b,X0)) = X0,
inference(forward_demodulation,[],[f516,f40]) ).
fof(f552,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f39,f438]) ).
fof(f628,plain,
inverse(b) = greatest_lower_bound(inverse(b),identity),
inference(superposition,[],[f528,f552]) ).
fof(f641,plain,
inverse(b) = greatest_lower_bound(identity,inverse(b)),
inference(forward_demodulation,[],[f628,f5]) ).
fof(f647,plain,
identity = least_upper_bound(identity,inverse(b)),
inference(superposition,[],[f11,f641]) ).
fof(f649,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(inverse(b),X0)),
inference(superposition,[],[f47,f647]) ).
fof(f652,plain,
! [X0] : least_upper_bound(X0,multiply(inverse(b),X0)) = X0,
inference(forward_demodulation,[],[f649,f40]) ).
fof(f706,plain,
sF4 = least_upper_bound(sF4,a),
inference(superposition,[],[f652,f102]) ).
fof(f728,plain,
sF4 = least_upper_bound(a,sF4),
inference(forward_demodulation,[],[f706,f6]) ).
fof(f1947,plain,
multiply(inverse(inverse(sF3)),least_upper_bound(inverse(sF3),sF4)) = least_upper_bound(identity,sF5),
inference(superposition,[],[f58,f159]) ).
fof(f2003,plain,
least_upper_bound(identity,sF5) = multiply(inverse(inverse(sF3)),least_upper_bound(sF4,inverse(sF3))),
inference(forward_demodulation,[],[f1947,f6]) ).
fof(f2026,plain,
least_upper_bound(identity,sF5) = multiply(inverse(a),least_upper_bound(sF4,a)),
inference(forward_demodulation,[],[f2003,f320]) ).
fof(f2034,plain,
multiply(inverse(a),least_upper_bound(a,sF4)) = least_upper_bound(identity,sF5),
inference(forward_demodulation,[],[f2026,f6]) ).
fof(f2037,plain,
multiply(inverse(a),sF4) = least_upper_bound(identity,sF5),
inference(forward_demodulation,[],[f2034,f728]) ).
fof(f2040,plain,
multiply(sF3,sF4) = least_upper_bound(identity,sF5),
inference(forward_demodulation,[],[f2037,f31]) ).
fof(f2041,plain,
sF5 = least_upper_bound(identity,sF5),
inference(forward_demodulation,[],[f2040,f35]) ).
fof(f2047,plain,
identity = greatest_lower_bound(identity,sF5),
inference(superposition,[],[f12,f2041]) ).
fof(f2049,plain,
identity = sF6,
inference(forward_demodulation,[],[f2047,f37]) ).
fof(f2051,plain,
identity != identity,
inference(superposition,[],[f38,f2049]) ).
fof(f2064,plain,
$false,
inference(trivial_inequality_removal,[],[f2051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP175-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:40:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.57/1.31 % (2369647)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.57/1.31 % (2369805)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=333472894:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.57/1.31 % (2369810)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1340083494:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.57/1.31 % (2369807)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2987719332:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.57/1.31 % (2369804)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=432395441:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.57/1.31 % (2369806)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2102078136:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.57/1.31 % (2369808)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1717276743:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.57/1.31 % (2369809)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=432614889:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.57/1.31 % (2369808)First to succeed.
% 1.57/1.31 % (2369808)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2369647"
% 1.57/1.31 % (2369807)Instruction limit reached!
% 1.57/1.31 % (2369807)------------------------------
% 1.57/1.31 % (2369807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.57/1.31 % (2369807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/1.31 % (2369807)CaDiCaL version: 2.1.3
% 1.57/1.31 % (2369807)Termination reason: Instruction limit
% 1.57/1.31 % (2369807)Termination phase: Saturation
% 1.57/1.31 % (2369807)Time elapsed: 0.084 s
% 1.57/1.31 % (2369807)Peak memory usage: 89 MB
% 1.57/1.31 % (2369807)Instructions burned: 136 (million)
% 1.57/1.31 % (2369810)Also succeeded, but the first one will report.
% 1.57/1.31 % (2369809)Instruction limit reached!
% 1.57/1.31 % (2369809)------------------------------
% 1.57/1.31 % (2369809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.57/1.31 % (2369809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/1.31 % (2369809)CaDiCaL version: 2.1.3
% 1.57/1.31 % (2369809)Termination reason: Instruction limit
% 1.57/1.31 % (2369809)Termination phase: Saturation
% 1.57/1.31 % (2369809)Time elapsed: 0.165 s
% 1.57/1.31 % (2369809)Peak memory usage: 91 MB
% 1.57/1.31 % (2369809)Instructions burned: 257 (million)
% 1.57/1.31 % (2369818)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1929107790:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 1.57/1.31 % (2369808)Refutation found. Thanks to Tanya!
% 1.57/1.31 % SZS status Unsatisfiable for theBenchmark
% 1.57/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.41 % (2369808)------------------------------
% 3.78/1.41 % (2369808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.41 % (2369808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.41 % (2369808)CaDiCaL version: 2.1.3
% 3.78/1.41 % (2369808)Termination reason: Refutation
% 3.78/1.41 % (2369808)Time elapsed: 0.044 s
% 3.78/1.41 % (2369808)Peak memory usage: 89 MB
% 3.78/1.41 % (2369808)Instructions burned: 70 (million)
% 3.78/1.41 % (2369808)------------------------------
% 3.78/1.41 % (2369808)------------------------------
% 3.78/1.41 % (2369647)Success in time 0.459 s
% 3.78/1.41 % Vampire exiting
%------------------------------------------------------------------------------