%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP179-3 : 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 : n006.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 04:24:42 PM UTC 2026
% Result : Unsatisfiable 4.58s 3.42s
% Output : CNFRefutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 6 RR)
% Number of literals : 64 ( 63 equ; 3 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; 2 con; 0-2 aty)
% Number of variables : 115 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(p18_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_2) ).
cnf(p18_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_3) ).
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_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
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(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(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(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
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(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(p18_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18_1) ).
cnf(prove_p18,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p18) ).
cnf(c_0_15,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_16,hypothesis,
inverse(inverse(X1)) = X1,
p18_2 ).
cnf(c_0_17,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p18_3 ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_19,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_22,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_23,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_24,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_25,hypothesis,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_26,hypothesis,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_27,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_20]) ).
cnf(c_0_30,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_31,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_16]) ).
cnf(c_0_32,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub ).
cnf(c_0_33,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]) ).
cnf(c_0_34,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_15]),c_0_16]) ).
cnf(c_0_36,hypothesis,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_24]) ).
cnf(c_0_38,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_15]),c_0_24]) ).
cnf(c_0_39,plain,
least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_40,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]),c_0_32]) ).
cnf(c_0_41,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22]) ).
cnf(c_0_42,hypothesis,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_22]) ).
cnf(c_0_43,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_44,hypothesis,
multiply(least_upper_bound(X1,multiply(X2,X3)),inverse(X3)) = least_upper_bound(multiply(X1,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_17]),c_0_16]),c_0_16]) ).
cnf(c_0_45,hypothesis,
multiply(least_upper_bound(X1,identity),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_24]) ).
cnf(c_0_46,plain,
multiply(least_upper_bound(X1,least_upper_bound(X2,inverse(X3))),X3) = least_upper_bound(identity,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_47,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_32]),c_0_32]),c_0_40]) ).
cnf(c_0_48,plain,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_15]),c_0_22]) ).
cnf(c_0_49,hypothesis,
multiply(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,inverse(X1)))) = greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X2,X3))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,hypothesis,
least_upper_bound(X1,least_upper_bound(identity,multiply(X2,X1))) = least_upper_bound(identity,multiply(least_upper_bound(X2,identity),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_16]),c_0_46]),c_0_16]),c_0_47]),c_0_24]) ).
cnf(c_0_51,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_22]) ).
cnf(c_0_52,hypothesis,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(X1,greatest_lower_bound(identity,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_22]),c_0_49]) ).
cnf(c_0_53,hypothesis,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_54,hypothesis,
least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_21]),c_0_24]),c_0_21]),c_0_24]) ).
cnf(c_0_55,hypothesis,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_22]),c_0_23]),c_0_22]),c_0_23]) ).
cnf(c_0_56,hypothesis,
least_upper_bound(identity,multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) = identity,
inference(spm,[status(thm)],[c_0_54,c_0_16]) ).
cnf(c_0_57,hypothesis,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_55]),c_0_24]),c_0_56]) ).
cnf(c_0_58,hypothesis,
inverse(identity) = identity,
p18_1 ).
cnf(c_0_59,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
prove_p18 ).
cnf(c_0_60,hypothesis,
inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_57]),c_0_58]),c_0_20]) ).
cnf(c_0_61,negated_conjecture,
least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(identity,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_24]) ).
cnf(c_0_62,hypothesis,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_16]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP179-3 : 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:27:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.58/3.42 % Version : CSE_E---1.7
% 4.58/3.42 % Problem : theBenchmark.p
% 4.58/3.42 % SZS status Unsatisfiable for theBenchmark.p
% 4.58/3.42 % SZS output start CNFRefutation
% See solution above
% 4.58/3.43 % Total time : 2.372s
%------------------------------------------------------------------------------