%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP167-5 : 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 : n024.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 04:24:38 PM UTC 2026
% Result : Unsatisfiable 1.15s 1.63s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 6 RR)
% Number of literals : 41 ( 40 equ; 4 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 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(p10,axiom,
inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
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_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat4) ).
cnf(lat4_1,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_1) ).
cnf(lat4_2,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_2) ).
cnf(c_0_10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_11,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_12,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_13,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_16,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
p10 ).
cnf(c_0_20,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_21,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_24,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_26,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_27,plain,
inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(X1,identity),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
prove_lat4 ).
cnf(c_0_31,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
lat4_1 ).
cnf(c_0_32,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
lat4_2 ).
cnf(c_0_33,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_34,plain,
multiply(X1,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_18]) ).
cnf(c_0_35,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_33]),c_0_18]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),least_upper_bound(identity,X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_21]),c_0_26]) ).
cnf(c_0_39,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_22]),c_0_22]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP167-5 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 13:26:11 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.15/1.63 % Version : CSE_E---1.7
% 1.15/1.63 % Problem : theBenchmark.p
% 1.15/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 1.15/1.63 % SZS output start CNFRefutation
% See solution above
% 1.15/1.63 % Total time : 1.361s
%------------------------------------------------------------------------------