%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP169-1 : 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 10:13:09 AM UTC 2026
% Result : Unsatisfiable 4.14s 1.53s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 44 unt; 1 def)
% Number of atoms : 44 ( 40 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_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(f17,axiom,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02a_1) ).
fof(f18,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(a,b) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02a) ).
fof(f20,plain,
a != least_upper_bound(a,b),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
~ sP0(least_upper_bound(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f22,plain,
sP0(a),
inference(inequality_splitting,[],[f20,f21]) ).
fof(f25,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f37,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(superposition,[],[f12,f18]) ).
fof(f50,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f53,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f50,f1]) ).
fof(f55,plain,
inverse(b) = least_upper_bound(inverse(b),inverse(a)),
inference(superposition,[],[f25,f37]) ).
fof(f81,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f53,f3]) ).
fof(f83,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f53,f53]) ).
fof(f86,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f81,f83]) ).
fof(f87,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)),
inference(superposition,[],[f8,f9]) ).
fof(f190,plain,
! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f15,f3]) ).
fof(f285,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,X1)),
inference(superposition,[],[f87,f6]) ).
fof(f734,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f86,f83]) ).
fof(f735,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f53,f83]) ).
fof(f738,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f734,f86]) ).
fof(f1040,plain,
! [X2,X0,X1] : multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X0))) = least_upper_bound(multiply(X1,X2),X0),
inference(superposition,[],[f13,f735]) ).
fof(f1494,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(b),b),
inference(superposition,[],[f190,f55]) ).
fof(f1536,plain,
identity = least_upper_bound(identity,multiply(inverse(a),b)),
inference(forward_demodulation,[],[f1494,f3]) ).
fof(f1935,plain,
identity = least_upper_bound(multiply(inverse(a),b),identity),
inference(superposition,[],[f285,f1536]) ).
fof(f1986,plain,
identity = multiply(inverse(a),least_upper_bound(b,multiply(inverse(inverse(a)),identity))),
inference(forward_demodulation,[],[f1935,f1040]) ).
fof(f1995,plain,
identity = multiply(inverse(a),least_upper_bound(b,inverse(inverse(a)))),
inference(forward_demodulation,[],[f1986,f86]) ).
fof(f2000,plain,
identity = multiply(inverse(a),least_upper_bound(b,a)),
inference(forward_demodulation,[],[f1995,f738]) ).
fof(f2630,plain,
least_upper_bound(b,a) = multiply(a,identity),
inference(superposition,[],[f735,f2000]) ).
fof(f2641,plain,
a = least_upper_bound(b,a),
inference(forward_demodulation,[],[f2630,f86]) ).
fof(f2760,plain,
a = least_upper_bound(a,b),
inference(superposition,[],[f6,f2641]) ).
fof(f2789,plain,
~ sP0(a),
inference(backward_demodulation,[],[f21,f2760]) ).
fof(f2790,plain,
$false,
inference(forward_subsumption_resolution,[],[f2789,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:36:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 4.14/1.53 % (250970)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.14/1.53 % (250980)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=991001782:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.14/1.53 % (250977)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3248195095:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.14/1.53 % (250976)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=1855404273:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.14/1.53 % (250975)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=1617722164:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.14/1.53 % (250978)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2643822632:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.14/1.53 % (250979)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=338745295:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.14/1.53 % (250981)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2452804305:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.14/1.53 % (250980)Instruction limit reached!
% 4.14/1.53 % (250980)------------------------------
% 4.14/1.53 % (250980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.53 % (250980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.53 % (250980)CaDiCaL version: 2.1.3
% 4.14/1.53 % (250980)Termination reason: Instruction limit
% 4.14/1.53 % (250980)Termination phase: Saturation
% 4.14/1.53 % (250980)Time elapsed: 0.087 s
% 4.14/1.53 % (250980)Peak memory usage: 91 MB
% 4.14/1.53 % (250980)Instructions burned: 260 (million)
% 4.14/1.53 % (250978)First to succeed.
% 4.14/1.53 % (250978)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-250970"
% 4.14/1.53 % (250979)Also succeeded, but the first one will report.
% 4.14/1.53 % (250981)Also succeeded, but the first one will report.
% 4.14/1.53 % (250989)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=484595844:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.14/1.53 % (250978)Refutation found. Thanks to Tanya!
% 4.14/1.53 % SZS status Unsatisfiable for theBenchmark
% 4.14/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.14/1.53 % (250978)------------------------------
% 4.14/1.53 % (250978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.53 % (250978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.53 % (250978)CaDiCaL version: 2.1.3
% 4.14/1.53 % (250978)Termination reason: Refutation
% 4.14/1.53 % (250978)Time elapsed: 0.076 s
% 4.14/1.53 % (250978)Peak memory usage: 89 MB
% 4.14/1.53 % (250978)Instructions burned: 122 (million)
% 4.14/1.53 % (250978)------------------------------
% 4.14/1.53 % (250978)------------------------------
% 4.14/1.53 % (250970)Success in time 0.498 s
% 4.14/1.53 % Vampire exiting
%------------------------------------------------------------------------------