%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP192-1 : 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 : n003.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 2 neg)
% Maximal clause size : 1 ( 1 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 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(p40a_1,hypothesis,
least_upper_bound(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40a_1) ).
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(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(prove_p40a,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p40a) ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_9,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_10,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_11,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_12,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_13,hypothesis,
least_upper_bound(identity,X1) = X1,
p40a_1 ).
cnf(c_0_14,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_16,hypothesis,
greatest_lower_bound(identity,X1) = identity,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_18,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_20,hypothesis,
greatest_lower_bound(X1,identity) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]),c_0_18]),c_0_17]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_21]) ).
cnf(c_0_24,plain,
inverse(X1) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
multiply(a,b) != multiply(b,a),
prove_p40a ).
cnf(c_0_26,plain,
X1 = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP192-1 : 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:27:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------