%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD038-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 04:18:20 PM UTC 2026
% Result : Unsatisfiable 2.20s 2.01s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 81 ( 36 unt; 4 nHn; 81 RR)
% Number of literals : 150 ( 0 equ; 70 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(multiplicative_identity_equals_multiply_4,negated_conjecture,
equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity_equals_multiply_4) ).
cnf(a_not_equal_to_b_5,negated_conjecture,
~ equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_b_5) ).
cnf(c_0_16,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_17,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_18,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_3 ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_22,hypothesis,
equalish(multiply(multiplicative_identity,b),b),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_24,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,hypothesis,
equalish(multiply(multiplicative_identity,a),a),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_26,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_27,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,multiply(multiplicative_identity,b)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiplicative_identity,a)) ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_30,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_31,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_32,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_33,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_34,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_35,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_19])]) ).
cnf(c_0_36,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_37,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),b)) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_38,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_20]) ).
cnf(c_0_40,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),a)) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_41,hypothesis,
( equalish(multiply(X1,X2),multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_42,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_43,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_44,hypothesis,
equalish(multiply(b,multiply(a,multiplicative_inverse(a))),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_17]),c_0_39]),c_0_19])]) ).
cnf(c_0_45,hypothesis,
( equalish(multiply(X1,a),a)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_19])]) ).
cnf(c_0_46,plain,
( equalish(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_42]) ).
cnf(c_0_47,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_48,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_49,hypothesis,
equalish(b,multiply(b,multiply(a,multiplicative_inverse(a)))),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(X2,a))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_51,hypothesis,
equalish(multiply(a,multiplicative_identity),multiply(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_52,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_53,hypothesis,
equalish(b,multiply(multiplicative_identity,b)),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_54,hypothesis,
equalish(b,multiply(multiply(b,a),multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39]),c_0_19]),c_0_17])]) ).
cnf(c_0_55,hypothesis,
equalish(multiply(a,multiplicative_identity),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_56,hypothesis,
( equalish(X1,multiply(multiplicative_identity,b))
| ~ equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_57,hypothesis,
equalish(multiply(multiply(b,a),multiplicative_inverse(a)),b),
inference(spm,[status(thm)],[c_0_26,c_0_54]) ).
cnf(c_0_58,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(a,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_59,hypothesis,
( equalish(multiply(multiplicative_identity,b),X1)
| ~ equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_60,hypothesis,
equalish(a,multiply(a,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_26,c_0_55]) ).
cnf(c_0_61,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,multiply(multiply(b,a),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
multiplicative_identity_equals_multiply_4 ).
cnf(c_0_63,hypothesis,
( equalish(multiply(multiplicative_identity,b),a)
| ~ equalish(multiply(a,multiplicative_identity),b) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,hypothesis,
( equalish(X1,multiply(a,multiplicative_identity))
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_21,c_0_60]) ).
cnf(c_0_65,hypothesis,
equalish(multiply(multiplicative_inverse(a),multiply(b,a)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_39]),c_0_19]),c_0_17])]) ).
cnf(c_0_66,negated_conjecture,
equalish(multiply(b,multiplicative_inverse(a)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_26,c_0_62]) ).
cnf(c_0_67,hypothesis,
( equalish(multiply(X1,b),multiply(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_68,hypothesis,
( equalish(multiply(X1,b),b)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_17])]) ).
cnf(c_0_69,hypothesis,
( equalish(a,multiply(multiplicative_identity,b))
| ~ equalish(multiply(a,multiplicative_identity),b) ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_70,hypothesis,
( equalish(multiply(a,multiplicative_identity),X1)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_71,hypothesis,
equalish(b,multiply(multiplicative_inverse(a),multiply(b,a))),
inference(spm,[status(thm)],[c_0_26,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(b,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_66]) ).
cnf(c_0_73,hypothesis,
equalish(multiply(multiplicative_inverse(a),b),multiply(b,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_74,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,multiply(X2,b))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_68]) ).
cnf(c_0_75,hypothesis,
( equalish(a,multiply(multiplicative_identity,b))
| ~ equalish(b,a) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
~ equalish(a,b),
a_not_equal_to_b_5 ).
cnf(c_0_77,hypothesis,
equalish(b,multiply(multiply(multiplicative_inverse(a),b),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_71]),c_0_19]),c_0_17]),c_0_39])]) ).
cnf(c_0_78,negated_conjecture,
equalish(multiply(multiplicative_inverse(a),b),multiplicative_identity),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,hypothesis,
~ equalish(b,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_52])]),c_0_76]) ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_77]),c_0_78])]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD038-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n004.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 17:27:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.20/2.01 % Version : CSE_E---1.7
% 2.20/2.01 % Problem : theBenchmark.p
% 2.20/2.01 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/2.01 % SZS output start CNFRefutation
% See solution above
% 2.20/2.01 % Total time : 1.367s
%------------------------------------------------------------------------------