%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD031-1 : 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 : n021.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 8.34s 5.89s
% Output : CNFRefutation 8.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of clauses : 67 ( 29 unt; 9 nHn; 67 RR)
% Number of literals : 116 ( 0 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
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(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(a_equals_multiplicative_identity_2,negated_conjecture,
equalish(a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_multiplicative_identity_2) ).
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
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(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_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(multiplicative_inverses_not_equal,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_not_equal) ).
cnf(c_0_14,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_15,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_16,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_3 ).
cnf(c_0_17,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_18,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_20,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_23,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_24,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_25,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_26,hypothesis,
( equalish(X1,X2)
| ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
equalish(a,multiplicative_identity),
a_equals_multiplicative_identity_2 ).
cnf(c_0_28,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_31,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( equalish(a,X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_33,plain,
( equalish(X1,add(additive_identity,additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_34,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_35,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_36,negated_conjecture,
~ equalish(add(additive_identity,additive_identity),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_16]) ).
cnf(c_0_37,plain,
( equalish(add(additive_identity,additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_38,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_39,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity)
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
~ equalish(multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity),
inference(sr,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_45,plain,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))) ),
inference(spm,[status(thm)],[c_0_19,c_0_43]) ).
cnf(c_0_46,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))),
inference(sr,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_47,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_48,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_49,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiplicative_inverse(multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_53,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_15]),c_0_16]) ).
cnf(c_0_54,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_55,negated_conjecture,
equalish(multiplicative_inverse(multiplicative_identity),a),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_57,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_58,negated_conjecture,
( equalish(multiply(multiplicative_inverse(multiplicative_identity),X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_60,plain,
( equalish(multiply(multiplicative_inverse(multiplicative_identity),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_61,hypothesis,
equalish(multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53])]) ).
cnf(c_0_62,hypothesis,
equalish(multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_53])]) ).
cnf(c_0_63,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_19,c_0_61]) ).
cnf(c_0_64,hypothesis,
equalish(multiplicative_inverse(a),multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_17,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
multiplicative_inverses_not_equal ).
cnf(c_0_66,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD031-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:28:10 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 8.34/5.89 % Version : CSE_E---1.7
% 8.34/5.89 % Problem : theBenchmark.p
% 8.34/5.89 % SZS status Unsatisfiable for theBenchmark.p
% 8.34/5.89 % SZS output start CNFRefutation
% See solution above
% 8.45/5.92 % Total time : 4.372s
%------------------------------------------------------------------------------