%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD029-3 : 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 : n010.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 04:18:17 PM UTC 2026
% Result : Unsatisfiable 6.58s 4.68s
% Output : CNFRefutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 51 ( 21 unt; 4 nHn; 51 RR)
% Number of literals : 105 ( 0 equ; 54 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(product_7,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
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(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(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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
cnf(product_6,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
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(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
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(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).
cnf(c_0_14,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_15,negated_conjecture,
product(a,v,b),
product_7 ).
cnf(c_0_16,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_17,negated_conjecture,
( product(X1,X2,b)
| ~ product(X3,v,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( product(X1,v,X2)
| ~ product(X3,b,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_20,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_21,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_22,negated_conjecture,
( product(X1,b,b)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_24,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_25,negated_conjecture,
( product(X1,v,multiply(X2,b))
| ~ product(X2,a,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
product(v,a,b),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_27,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_28,negated_conjecture,
product(multiplicative_identity,b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_29,negated_conjecture,
product(a,u,b),
product_6 ).
cnf(c_0_30,negated_conjecture,
product(b,v,multiply(v,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,b,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_32,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_33,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_5 ).
cnf(c_0_34,negated_conjecture,
( product(X1,u,X2)
| ~ product(X3,b,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
product(v,b,multiply(v,b)),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( product(X1,b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]),c_0_33]) ).
cnf(c_0_37,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_38,negated_conjecture,
( product(X1,u,multiply(v,b))
| ~ product(v,a,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_41,negated_conjecture,
product(b,u,multiply(v,b)),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_42,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_43,negated_conjecture,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20])]),c_0_33]) ).
cnf(c_0_44,negated_conjecture,
( product(X1,u,X2)
| ~ product(X3,multiply(v,b),X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( product(multiplicative_inverse(b),X1,X2)
| ~ product(b,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
( product(X1,X2,multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_47,negated_conjecture,
( product(multiplicative_identity,u,X1)
| ~ product(multiplicative_inverse(b),multiply(v,b),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_20])]),c_0_33]) ).
cnf(c_0_48,negated_conjecture,
( product(multiplicative_inverse(b),multiply(X1,b),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_20])]) ).
cnf(c_0_49,negated_conjecture,
~ product(multiplicative_identity,u,v),
not_product_8 ).
cnf(c_0_50,negated_conjecture,
$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_27])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD029-3 : 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
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:27:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 6.58/4.68 % Version : CSE_E---1.7
% 6.58/4.68 % Problem : theBenchmark.p
% 6.58/4.68 % SZS status Unsatisfiable for theBenchmark.p
% 6.58/4.68 % SZS output start CNFRefutation
% See solution above
% 6.68/4.71 % Total time : 3.371s
%------------------------------------------------------------------------------