%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD037-3 : 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 : n018.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 04:18:20 PM UTC 2026
% Result : Unsatisfiable 0.29s 1.62s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of clauses : 78 ( 22 unt; 8 nHn; 78 RR)
% Number of literals : 197 ( 0 equ; 120 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 164 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity_2,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
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(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(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X3)
| ~ product(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_multiplication) ).
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(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
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(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(not_product_5,negated_conjecture,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_5) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
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(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
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(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(product_4,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_4) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(i_0_31,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
distributivity_2,
[final] ).
cnf(i_0_32,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
distributivity_1,
[final] ).
cnf(i_0_33,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2,
[final] ).
cnf(i_0_34,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1,
[final] ).
cnf(i_0_35,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2,
[final] ).
cnf(i_0_36,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1,
[final] ).
cnf(i_0_37,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition,
[final] ).
cnf(i_0_38,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication,
[final] ).
cnf(i_0_39,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition,
[final] ).
cnf(i_0_40,axiom,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X3)
| ~ product(X2,X3,X1) ),
compatibility_of_order_relation_and_multiplication,
[final] ).
cnf(i_0_41,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication,
[final] ).
cnf(i_0_42,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation,
[final] ).
cnf(i_0_43,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication,
[final] ).
cnf(i_0_44,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition,
[final] ).
cnf(i_0_45,negated_conjecture,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
not_product_5,
[final] ).
cnf(i_0_46,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_3,
[final] ).
cnf(i_0_47,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities,
[final] ).
cnf(i_0_48,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_49,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition,
[final] ).
cnf(i_0_50,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication,
[final] ).
cnf(i_0_51,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition,
[final] ).
cnf(i_0_52,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation,
[final] ).
cnf(i_0_53,negated_conjecture,
product(multiplicative_identity,a,b),
product_4,
[final] ).
cnf(i_0_54,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication,
[final] ).
cnf(i_0_55,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition,
[final] ).
cnf(i_0_56,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation,
[final] ).
cnf(i_0_57,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse,
[final] ).
cnf(i_0_58,hypothesis,
defined(b),
b_is_defined,
[final] ).
cnf(i_0_59,hypothesis,
defined(a),
a_is_defined,
[final] ).
cnf(i_0_60,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity,
[final] ).
cnf(i_0_61,axiom,
defined(additive_identity),
well_definedness_of_additive_identity,
[final] ).
cnf(i_0_62,plain,
product(a,multiplicative_identity,b),
inference(scs_inference,[],[i_0_53,i_0_38]) ).
cnf(i_0_63,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_64,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(scs_inference,[],[i_0_46,i_0_53,i_0_59,i_0_38,i_0_41]) ).
cnf(i_0_65,plain,
( sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity)
| ~ defined(X1) ),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_66,plain,
( ~ less_or_equal(a,additive_identity)
| ~ less_or_equal(additive_identity,a) ),
inference(scs_inference,[],[i_0_46,i_0_53,i_0_59,i_0_38,i_0_41,i_0_42]) ).
cnf(i_0_67,plain,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_68,plain,
( ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,a) ),
inference(scs_inference,[],[i_0_46,i_0_53,i_0_59,i_0_61,i_0_38,i_0_41,i_0_42,i_0_56]) ).
cnf(i_0_69,plain,
( less_or_equal(X1,X2)
| ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1) ),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_70,plain,
( ~ less_or_equal(additive_identity,a)
| sum(b,b,b)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(scs_inference,[],[i_0_46,i_0_53,i_0_59,i_0_61,i_0_38,i_0_41,i_0_42,i_0_56,i_0_32]) ).
cnf(i_0_71,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(scs_inference,[],[i_0_64,i_0_38]) ).
cnf(i_0_72,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_73,plain,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(scs_inference,[],[i_0_45,i_0_64,i_0_62,i_0_38,i_0_33]) ).
cnf(i_0_74,plain,
( ~ product(X1,X2,X3)
| product(X4,X5,X3)
| ~ product(X1,X6,X4)
| ~ product(X6,X5,X2) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_75,plain,
~ defined(multiplicative_inverse(a)),
inference(scs_inference,[],[i_0_45,i_0_64,i_0_62,i_0_38,i_0_33,i_0_50]) ).
cnf(i_0_76,plain,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_77,plain,
$false,
inference(scs_inference,[],[i_0_45,i_0_46,i_0_64,i_0_62,i_0_59,i_0_38,i_0_33,i_0_50,i_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD037-3 : 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
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:28:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.29/1.62 % Version : CSE_E---1.7
% 0.29/1.62 % Problem : theBenchmark.p
% 0.29/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.29/1.62 % SZS output start CNFRefutation
% See solution above
% 0.29/1.66 % Total time : 1.272s
%------------------------------------------------------------------------------