%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP193-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:24:47 PM UTC 2026
% Result : Unsatisfiable 1.60s 1.84s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 12 RR)
% Number of literals : 25 ( 24 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p8_9b_5,hypothesis,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_5) ).
cnf(p8_9b_4,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_4) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(p8_9b_2,hypothesis,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_9b_2) ).
cnf(prove_p8_9b,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p8_9b) ).
cnf(c_0_9,hypothesis,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
p8_9b_5 ).
cnf(c_0_10,hypothesis,
greatest_lower_bound(a,b) = identity,
p8_9b_4 ).
cnf(c_0_11,hypothesis,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(identity,greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_13,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_14,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_15,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_16,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_17,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_13]) ).
cnf(c_0_18,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_19,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_20,hypothesis,
greatest_lower_bound(identity,b) = identity,
p8_9b_2 ).
cnf(c_0_21,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,hypothesis,
greatest_lower_bound(X1,multiply(b,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12]) ).
cnf(c_0_23,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
prove_p8_9b ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP193-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 18:28:48 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.60/1.84 % Version : CSE_E---1.7
% 1.60/1.84 % Problem : theBenchmark.p
% 1.60/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.60/1.84 % SZS output start CNFRefutation
% See solution above
% 1.60/1.84 % Total time : 1.371s
%------------------------------------------------------------------------------