%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP193-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 1.45s 1.80s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 12 RR)
% Number of literals : 31 ( 30 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; 4 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p8_9a_5,hypothesis,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9a_5) ).
cnf(p8_9a_4,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9a_4) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(prove_p8_9a,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p8_9a) ).
cnf(c_0_10,hypothesis,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
p8_9a_5 ).
cnf(c_0_11,hypothesis,
greatest_lower_bound(a,b) = identity,
p8_9a_4 ).
cnf(c_0_12,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_13,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_14,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_15,hypothesis,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,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_19,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_20,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_21,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_25,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_26,hypothesis,
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)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_19]) ).
cnf(c_0_28,hypothesis,
greatest_lower_bound(b,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_11]),c_0_19]) ).
cnf(c_0_29,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
prove_p8_9a ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_12]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP193-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:27:47 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.45/1.80 % Version : CSE_E---1.7
% 1.45/1.80 % Problem : theBenchmark.p
% 1.45/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.45/1.80 % SZS output start CNFRefutation
% See solution above
% 1.56/1.80 % Total time : 1.371s
%------------------------------------------------------------------------------