%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 10:17:01 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',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/Axioms/GRP004-2.ax',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/Axioms/GRP004-2.ax',monotony_lub2) ).
fof(f17,axiom,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02b_1) ).
fof(f18,plain,
inverse(a) = greatest_lower_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02b) ).
fof(f20,plain,
b != greatest_lower_bound(a,b),
inference(reorient_equations,[],[f19]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f26,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f34,plain,
inverse(b) = least_upper_bound(inverse(b),inverse(a)),
inference(superposition,[],[f23,f18]) ).
fof(f36,plain,
inverse(b) = least_upper_bound(inverse(a),inverse(b)),
inference(forward_demodulation,[],[f34,f6]) ).
fof(f39,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f42,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f39,f1]) ).
fof(f78,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f42,f3]) ).
fof(f80,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f42,f42]) ).
fof(f83,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f78,f80]) ).
fof(f113,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f200,plain,
! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(multiply(X0,X1),identity),
inference(superposition,[],[f15,f3]) ).
fof(f223,plain,
! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(identity,multiply(X0,X1)),
inference(forward_demodulation,[],[f200,f6]) ).
fof(f782,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f42,f80]) ).
fof(f1604,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(b),b),
inference(superposition,[],[f223,f36]) ).
fof(f1633,plain,
identity = least_upper_bound(identity,multiply(inverse(a),b)),
inference(forward_demodulation,[],[f1604,f3]) ).
fof(f1641,plain,
identity = multiply(inverse(a),least_upper_bound(a,b)),
inference(forward_demodulation,[],[f1633,f113]) ).
fof(f1645,plain,
least_upper_bound(a,b) = multiply(a,identity),
inference(superposition,[],[f782,f1641]) ).
fof(f1672,plain,
a = least_upper_bound(a,b),
inference(forward_demodulation,[],[f1645,f83]) ).
fof(f1769,plain,
b = greatest_lower_bound(b,a),
inference(superposition,[],[f26,f1672]) ).
fof(f1781,plain,
b = greatest_lower_bound(a,b),
inference(forward_demodulation,[],[f1769,f5]) ).
fof(f1782,plain,
$false,
inference(forward_subsumption_resolution,[],[f1781,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n014.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 09:35:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.50 % (547395)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (547400)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=917043403_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % (547401)% WARNING: option uhcvi not known.
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % (547402)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1881374200:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (547401)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=342696913:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (547403)dis+10_1_sil=32000:sp=arity:random_seed=2161916825:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (547405)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2213667254:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (547404)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1663828114:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (547406)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2000361913:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % TRYING [5]
% 0.17/0.50 % (547404) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-547395-547404"...
% 0.17/0.50 % (547404)...printing done.
% 0.17/0.50 % (547404)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (547404)------------------------------
% 0.17/0.50 % (547404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (547404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (547404)CaDiCaL version: 2.1.3
% 0.17/0.50 % (547404)Termination reason: Refutation
% 0.17/0.50 % (547404)Time elapsed: 0.041 s
% 0.17/0.50 % (547404)Peak memory usage: 12 MB
% 0.17/0.50 % (547404)Instructions burned: 67 (million)
% 0.17/0.50 % (547395)Success in time 0.085 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------