%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD009-3 : 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 : n022.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 04:18:11 PM UTC 2026
% Result : Unsatisfiable 1.48s 1.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 15 unt; 4 nHn; 31 RR)
% Number of literals : 58 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(not_product_4,negated_conjecture,
~ product(a,X1,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_10,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_11,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_12,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_13,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_14,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_3 ).
cnf(c_0_15,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_16,hypothesis,
( product(X1,b,multiply(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_19,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_14]) ).
cnf(c_0_20,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_21,hypothesis,
product(multiplicative_inverse(a),b,multiply(multiplicative_inverse(a),b)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,hypothesis,
product(b,multiplicative_inverse(a),multiply(multiplicative_inverse(a),b)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_25,hypothesis,
( product(multiply(multiplicative_inverse(a),b),a,X1)
| ~ product(b,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_27,negated_conjecture,
~ product(a,X1,b),
not_product_4 ).
cnf(c_0_28,hypothesis,
( product(a,multiply(multiplicative_inverse(a),b),X1)
| ~ product(b,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD009-3 : 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
% 0.17/0.33 % Computer : n022.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 17:26:36 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.48/1.80 % Version : CSE_E---1.7
% 1.48/1.80 % Problem : theBenchmark.p
% 1.48/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.48/1.80 % SZS output start CNFRefutation
% See solution above
% 1.57/1.80 % Total time : 1.371s
%------------------------------------------------------------------------------