%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD033-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 : n020.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 04:18:18 PM UTC 2026
% Result : Unsatisfiable 1.72s 1.96s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 67 ( 27 unt; 4 nHn; 67 RR)
% Number of literals : 128 ( 0 equ; 63 neg)
% Maximal clause size : 4 ( 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 : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(m_is_defined,hypothesis,
defined(m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_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/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(multiply_equals_a_4,negated_conjecture,
equalish(multiply(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_a_4) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(m_not_equal_to_multiplicative_identity_5,negated_conjecture,
~ equalish(m,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_not_equal_to_multiplicative_identity_5) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(c_0_16,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_17,hypothesis,
defined(m),
m_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,m),m),
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,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_26,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(multiplicative_identity,m)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,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_28,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_29,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),m),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]) ).
cnf(c_0_30,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_31,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_32,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),m)) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_33,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_30]) ).
cnf(c_0_34,hypothesis,
( equalish(multiply(X1,m),multiply(m,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_35,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_36,hypothesis,
( equalish(multiply(X1,m),m)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17])]) ).
cnf(c_0_37,hypothesis,
equalish(multiply(multiplicative_identity,m),multiply(m,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_39,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(X2,m))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_40,hypothesis,
equalish(multiply(m,multiplicative_identity),multiply(multiplicative_identity,m)),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_41,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
equalish(multiply(m,a),a),
multiply_equals_a_4 ).
cnf(c_0_43,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_44,hypothesis,
equalish(multiply(m,multiplicative_identity),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_45,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( equalish(multiply(multiply(m,a),X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_47,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_20]) ).
cnf(c_0_48,hypothesis,
equalish(m,multiply(m,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_49,hypothesis,
equalish(multiply(multiply(m,a),multiplicative_inverse(a)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,multiply(m,multiplicative_identity))
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_51,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_52,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiply(m,a),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_53,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_54,hypothesis,
( equalish(multiply(m,multiplicative_identity),X1)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_55,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),m)
| ~ equalish(multiply(multiplicative_identity,m),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
cnf(c_0_56,hypothesis,
equalish(multiply(m,multiply(a,multiplicative_inverse(a))),multiplicative_identity),
inference(cn,[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_47]),c_0_19]),c_0_17])]) ).
cnf(c_0_57,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,multiply(m,multiplicative_identity))
| ~ equalish(X2,m) ),
inference(spm,[status(thm)],[c_0_21,c_0_54]) ).
cnf(c_0_58,hypothesis,
( equalish(m,multiply(a,multiplicative_inverse(a)))
| ~ equalish(multiply(multiplicative_identity,m),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
~ equalish(m,multiplicative_identity),
m_not_equal_to_multiplicative_identity_5 ).
cnf(c_0_60,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_61,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(m,multiply(a,multiplicative_inverse(a)))) ),
inference(spm,[status(thm)],[c_0_21,c_0_56]) ).
cnf(c_0_62,hypothesis,
( equalish(multiply(multiplicative_identity,m),X1)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_63,hypothesis,
~ equalish(multiply(multiplicative_identity,m),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_58]),c_0_59]) ).
cnf(c_0_64,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_60]) ).
cnf(c_0_65,hypothesis,
~ equalish(multiply(m,multiply(a,multiplicative_inverse(a))),m),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_66,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_64]),c_0_17]),c_0_47]),c_0_19])]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.17 % Problem : FLD033-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.07/0.17 % 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
% 0.16/0.38 % Computer : n020.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 4 17:28:04 EDT 2026
% 0.16/0.38 % CPUTime :
% 0.16/0.39 % start to proof: theBenchmark
% 1.72/1.96 % Version : CSE_E---1.7
% 1.72/1.96 % Problem : theBenchmark.p
% 1.72/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.72/1.96 % SZS output start CNFRefutation
% See solution above
% 1.72/1.97 % Total time : 1.385s
%------------------------------------------------------------------------------