%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD032-1 : 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 : 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 04:18:18 PM UTC 2026
% Result : Unsatisfiable 1.93s 1.92s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 18 unt; 4 nHn; 51 RR)
% Number of literals : 96 ( 0 equ; 47 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 : 45 ( 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_2,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_2) ).
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(multiplicative_inverses_equal,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_equal) ).
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(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(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(a_not_equal_to_multiplicative_identity_4,negated_conjecture,
~ equalish(a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_multiplicative_identity_4) ).
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(c_0_12,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_13,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_14,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_2 ).
cnf(c_0_15,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_16,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_18,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_21,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_22,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_23,hypothesis,
( equalish(X1,X2)
| ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_identity),
multiplicative_inverses_equal ).
cnf(c_0_25,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_28,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( equalish(multiplicative_inverse(a),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_30,hypothesis,
equalish(multiply(multiplicative_identity,a),a),
inference(spm,[status(thm)],[c_0_27,c_0_13]) ).
cnf(c_0_31,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_32,hypothesis,
equalish(a,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( equalish(multiplicative_inverse(a),a)
| ~ equalish(add(additive_identity,a),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiplicative_identity,a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( equalish(multiply(multiplicative_inverse(a),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_36,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_37,hypothesis,
( equalish(X1,add(additive_identity,a))
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_39,negated_conjecture,
( equalish(a,multiplicative_inverse(a))
| ~ equalish(add(additive_identity,a),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
~ equalish(a,multiplicative_identity),
a_not_equal_to_multiplicative_identity_4 ).
cnf(c_0_41,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_13])]) ).
cnf(c_0_42,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_43,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_13]),c_0_14]) ).
cnf(c_0_44,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_45,hypothesis,
( equalish(add(additive_identity,a),X1)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
~ equalish(add(additive_identity,a),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_47,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiplicative_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_48,hypothesis,
( equalish(multiply(X1,multiplicative_inverse(a)),multiply(multiplicative_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,hypothesis,
~ equalish(multiply(a,multiplicative_inverse(a)),a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_13])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD032-1 : 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 : n006.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 17:30:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.93/1.92 % Version : CSE_E---1.7
% 1.93/1.92 % Problem : theBenchmark.p
% 1.93/1.92 % SZS status Unsatisfiable for theBenchmark.p
% 1.93/1.92 % SZS output start CNFRefutation
% See solution above
% 1.93/1.92 % Total time : 1.369s
%------------------------------------------------------------------------------