%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP186-3 : 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 : n003.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 10:13:16 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.38s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 53 unt; 7 def)
% Number of atoms : 53 ( 52 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 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(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(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(f17,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p23x) ).
fof(f18,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f19]) ).
fof(f21,definition,
! [X0] : sF1(X0) = multiply(inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f22,plain,
! [X0] : multiply(inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0] : identity = sF1(X0),
inference(definition_folding,[],[f3,f22]) ).
fof(f24,definition,
sF2 = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f25,plain,
multiply(a,b) = sF2,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF3 = least_upper_bound(sF2,identity),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f27,plain,
least_upper_bound(sF2,identity) = sF3,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF4 = inverse(a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f29,plain,
inverse(a) = sF4,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF5 = least_upper_bound(sF4,b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f31,plain,
least_upper_bound(sF4,b) = sF5,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF6 = multiply(a,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f33,plain,
multiply(a,sF5) = sF6,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sF3 != sF6,
inference(definition_folding,[],[f17,f33,f31,f29,f27,f25]) ).
fof(f35,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f23,f22]) ).
fof(f36,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f20,f19]) ).
fof(f42,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0),
inference(superposition,[],[f15,f36]) ).
fof(f47,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f42,f6]) ).
fof(f52,plain,
identity = multiply(sF4,a),
inference(superposition,[],[f35,f29]) ).
fof(f53,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f35]) ).
fof(f54,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f35]) ).
fof(f66,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f53,f36]) ).
fof(f67,plain,
! [X0] : multiply(identity,X0) = multiply(sF4,multiply(a,X0)),
inference(superposition,[],[f4,f52]) ).
fof(f80,plain,
! [X0] : multiply(sF4,multiply(a,X0)) = X0,
inference(forward_demodulation,[],[f67,f36]) ).
fof(f81,plain,
sF5 = multiply(sF4,sF6),
inference(superposition,[],[f80,f33]) ).
fof(f82,plain,
b = multiply(sF4,sF2),
inference(superposition,[],[f80,f25]) ).
fof(f124,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f66,f35]) ).
fof(f130,plain,
sF2 = multiply(inverse(sF4),b),
inference(superposition,[],[f66,f82]) ).
fof(f131,plain,
sF6 = multiply(inverse(sF4),sF5),
inference(superposition,[],[f66,f81]) ).
fof(f217,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f66,f124]) ).
fof(f423,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f66,f217]) ).
fof(f424,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f423,f124]) ).
fof(f517,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f124,f424]) ).
fof(f904,plain,
! [X0] : least_upper_bound(X0,multiply(sF2,X0)) = multiply(sF3,X0),
inference(superposition,[],[f47,f27]) ).
fof(f1015,plain,
multiply(sF3,identity) = least_upper_bound(identity,sF2),
inference(superposition,[],[f904,f517]) ).
fof(f1036,plain,
sF3 = least_upper_bound(identity,sF2),
inference(forward_demodulation,[],[f1015,f517]) ).
fof(f1968,plain,
least_upper_bound(identity,sF2) = multiply(inverse(sF4),least_upper_bound(sF4,b)),
inference(superposition,[],[f54,f130]) ).
fof(f2018,plain,
multiply(inverse(sF4),sF5) = least_upper_bound(identity,sF2),
inference(forward_demodulation,[],[f1968,f31]) ).
fof(f2040,plain,
sF3 = multiply(inverse(sF4),sF5),
inference(forward_demodulation,[],[f2018,f1036]) ).
fof(f2050,plain,
sF3 = sF6,
inference(forward_demodulation,[],[f2040,f131]) ).
fof(f2055,plain,
sF3 != sF3,
inference(superposition,[],[f34,f2050]) ).
fof(f2063,plain,
$false,
inference(trivial_inequality_removal,[],[f2055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.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 09:38:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.78/1.38 % (253301)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.78/1.38 % (253310)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4116695920:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.78/1.38 % (253310)First to succeed.
% 2.78/1.38 % (253310)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-253301"
% 2.78/1.38 % (253308)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3421445602:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.78/1.38 % (253306)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=4139774782:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.78/1.38 % (253307)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=1887178944:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.78/1.38 % (253311)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=112021622:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.78/1.38 % (253309)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=229694552:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.78/1.38 % (253311)Also succeeded, but the first one will report.
% 2.78/1.38 % (253312)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4186795841:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.78/1.38 % (253309)Also succeeded, but the first one will report.
% 2.78/1.38 % (253310)Refutation found. Thanks to Tanya!
% 2.78/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.38 % (253310)------------------------------
% 2.78/1.38 % (253310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.38 % (253310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.38 % (253310)CaDiCaL version: 2.1.3
% 2.78/1.38 % (253310)Termination reason: Refutation
% 2.78/1.38 % (253310)Time elapsed: 0.023 s
% 2.78/1.38 % (253310)Peak memory usage: 89 MB
% 2.78/1.38 % (253310)Instructions burned: 69 (million)
% 2.78/1.38 % (253310)------------------------------
% 2.78/1.38 % (253310)------------------------------
% 2.78/1.38 % (253301)Success in time 0.317 s
% 2.78/1.38 % Vampire exiting
%------------------------------------------------------------------------------