%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD067-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:18:29 PM UTC 2026
% Result : Unsatisfiable 116.32s 86.01s
% Output : CNFRefutation 118.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_43210)
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(i_0_30,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_31,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_32,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2,
[final] ).
cnf(i_0_33,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1,
[final] ).
cnf(i_0_34,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2,
[final] ).
cnf(i_0_35,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1,
[final] ).
cnf(i_0_36,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_37,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication,
[final] ).
cnf(i_0_38,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition,
[final] ).
cnf(i_0_39,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_40,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication,
[final] ).
cnf(i_0_41,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation,
[final] ).
cnf(i_0_42,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication,
[final] ).
cnf(i_0_43,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition,
[final] ).
cnf(i_0_44,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities,
[final] ).
cnf(i_0_45,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_46,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition,
[final] ).
cnf(i_0_47,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
not_less_or_equal_4,
[final] ).
cnf(i_0_48,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication,
[final] ).
cnf(i_0_49,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition,
[final] ).
cnf(i_0_50,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation,
[final] ).
cnf(i_0_51,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication,
[final] ).
cnf(i_0_52,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition,
[final] ).
cnf(i_0_53,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation,
[final] ).
cnf(i_0_54,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse,
[final] ).
cnf(i_0_55,negated_conjecture,
less_or_equal(a,b),
less_or_equal_3,
[final] ).
cnf(i_0_56,hypothesis,
defined(b),
b_is_defined,
[final] ).
cnf(i_0_57,hypothesis,
defined(a),
a_is_defined,
[final] ).
cnf(i_0_58,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity,
[final] ).
cnf(i_0_59,axiom,
defined(additive_identity),
well_definedness_of_additive_identity,
[final] ).
cnf(i_0_43190,plain,
defined(additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54]) ).
cnf(i_0_43192,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48]) ).
cnf(i_0_43194,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49]) ).
cnf(i_0_43196,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46]) ).
cnf(i_0_43198,plain,
defined(multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51]) ).
cnf(i_0_43200,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42]) ).
cnf(i_0_43202,plain,
sum(additive_identity,additive_identity,add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43]) ).
cnf(i_0_43204,plain,
defined(add(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52]) ).
cnf(i_0_43206,plain,
less_or_equal(additive_identity,additive_identity),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53]) ).
cnf(i_0_43208,plain,
less_or_equal(additive_identity,multiply(additive_identity,additive_identity)),
inference(scs_inference,[],[i_0_59,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53,i_0_39]) ).
cnf(i_0_43214,plain,
~ less_or_equal(multiply(additive_identity,additive_identity),add(b,additive_inverse(a))),
inference(scs_inference,[],[i_0_47,i_0_59,i_0_56,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53,i_0_39,i_0_31,i_0_45,i_0_50]) ).
cnf(i_0_43216,plain,
~ sum(additive_identity,additive_identity,add(b,additive_inverse(a))),
inference(scs_inference,[],[i_0_47,i_0_59,i_0_56,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53,i_0_39,i_0_31,i_0_45,i_0_50,i_0_36]) ).
cnf(i_0_43220,plain,
~ sum(additive_inverse(additive_identity),additive_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_59,i_0_56,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53,i_0_39,i_0_31,i_0_45,i_0_50,i_0_36,i_0_33,i_0_34]) ).
cnf(i_0_43224,plain,
~ sum(additive_identity,additive_inverse(additive_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_59,i_0_56,i_0_54,i_0_48,i_0_49,i_0_46,i_0_51,i_0_42,i_0_43,i_0_52,i_0_53,i_0_39,i_0_31,i_0_45,i_0_50,i_0_36,i_0_33,i_0_34,i_0_30,i_0_38]) ).
cnf(i_0_43312,plain,
defined(additive_inverse(a)),
inference(scs_inference,[],[i_0_57,i_0_54]) ).
cnf(i_0_43794,plain,
product(multiplicative_identity,b,b),
inference(scs_inference,[],[i_0_56,i_0_48]) ).
cnf(i_0_43796,plain,
sum(additive_identity,b,b),
inference(scs_inference,[],[i_0_56,i_0_48,i_0_49]) ).
cnf(i_0_43947,plain,
product(multiplicative_identity,a,a),
inference(scs_inference,[],[i_0_57,i_0_48]) ).
cnf(i_0_43949,plain,
sum(additive_identity,a,a),
inference(scs_inference,[],[i_0_57,i_0_48,i_0_49]) ).
cnf(i_0_43228,plain,
defined(additive_inverse(add(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_43204,i_0_54]) ).
cnf(i_0_43236,plain,
defined(multiply(add(additive_identity,additive_identity),add(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_43204,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51]) ).
cnf(i_0_43242,plain,
defined(add(add(additive_identity,additive_identity),add(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_43204,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51,i_0_42,i_0_43,i_0_52]) ).
cnf(i_0_43244,plain,
~ sum(multiply(additive_identity,additive_identity),additive_identity,add(b,additive_inverse(a))),
inference(scs_inference,[],[i_0_47,i_0_43194,i_0_43204,i_0_43208,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51,i_0_42,i_0_43,i_0_52,i_0_36]) ).
cnf(i_0_43248,plain,
~ sum(additive_identity,multiply(additive_identity,additive_identity),add(b,additive_inverse(a))),
inference(scs_inference,[],[i_0_47,i_0_43194,i_0_43210,i_0_43204,i_0_43222,i_0_43208,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51,i_0_42,i_0_43,i_0_52,i_0_36,i_0_30,i_0_38]) ).
cnf(i_0_43255,plain,
defined(additive_inverse(additive_inverse(additive_identity))),
inference(scs_inference,[],[i_0_43190,i_0_54]) ).
cnf(i_0_43261,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_43190,i_0_54,i_0_48,i_0_46,i_0_49]) ).
cnf(i_0_43263,plain,
defined(multiply(additive_inverse(additive_identity),additive_inverse(additive_identity))),
inference(scs_inference,[],[i_0_43190,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51]) ).
cnf(i_0_43269,plain,
defined(add(additive_inverse(additive_identity),additive_inverse(additive_identity))),
inference(scs_inference,[],[i_0_43190,i_0_54,i_0_48,i_0_46,i_0_49,i_0_51,i_0_42,i_0_43,i_0_52]) ).
cnf(i_0_43284,plain,
defined(additive_inverse(multiply(additive_identity,additive_identity))),
inference(scs_inference,[],[i_0_43198,i_0_54]) ).
cnf(i_0_43344,plain,
less_or_equal(add(b,additive_inverse(a)),additive_identity),
inference(scs_inference,[],[i_0_43312,i_0_72]) ).
cnf(i_0_43373,plain,
product(multiplicative_identity,additive_inverse(a),additive_inverse(a)),
inference(scs_inference,[],[i_0_43312,i_0_48]) ).
cnf(i_0_43375,plain,
defined(additive_inverse(additive_inverse(a))),
inference(scs_inference,[],[i_0_43312,i_0_48,i_0_54]) ).
cnf(i_0_43377,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(scs_inference,[],[i_0_43312,i_0_48,i_0_54,i_0_49]) ).
cnf(i_0_43379,plain,
sum(additive_inverse(additive_inverse(a)),additive_inverse(a),additive_identity),
inference(scs_inference,[],[i_0_43312,i_0_48,i_0_54,i_0_49,i_0_46]) ).
cnf(i_0_44688,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(scs_inference,[],[i_0_43192,i_0_37]) ).
cnf(c_0_43390,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
i_0_35 ).
cnf(c_0_43391,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
i_0_46 ).
cnf(c_0_43392,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
i_0_38 ).
cnf(c_0_43393,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
i_0_43377 ).
cnf(c_0_43394,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X1,X4,additive_inverse(X3))
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_43390,c_0_43391]) ).
cnf(c_0_43395,plain,
sum(additive_inverse(a),additive_identity,additive_inverse(a)),
inference(spm,[status(thm)],[c_0_43392,c_0_43393]) ).
cnf(c_0_43396,hypothesis,
defined(a),
i_0_57 ).
cnf(c_0_43397,plain,
( sum(additive_inverse(a),X1,additive_identity)
| ~ sum(additive_identity,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43394,c_0_43395]),c_0_43396])]) ).
cnf(c_0_43398,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
i_0_49 ).
cnf(c_0_43399,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
i_0_36 ).
cnf(c_0_43400,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_43 ).
cnf(c_0_43401,plain,
sum(additive_inverse(a),a,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43397,c_0_43398]),c_0_43396])]) ).
cnf(c_0_43402,plain,
( less_or_equal(X1,add(X2,X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ less_or_equal(X4,X2)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_43399,c_0_43400]) ).
cnf(c_0_43403,plain,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_43392,c_0_43401]) ).
cnf(c_0_43404,plain,
defined(additive_inverse(a)),
i_0_43312 ).
cnf(c_0_43405,plain,
( less_or_equal(additive_identity,add(X1,additive_inverse(a)))
| ~ defined(X1)
| ~ less_or_equal(a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43402,c_0_43403]),c_0_43404])]) ).
cnf(c_0_43406,negated_conjecture,
less_or_equal(a,b),
i_0_55 ).
cnf(c_0_43407,hypothesis,
defined(b),
i_0_56 ).
cnf(c_0_43408,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
i_0_47 ).
cnf(c_0_43409,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43405,c_0_43406]),c_0_43407])]),c_0_43408]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD067-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n005.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 17:30:30 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 116.32/86.01 % Version : CSE_E---1.7
% 116.32/86.01 % Problem : theBenchmark.p
% 116.32/86.01 % SZS status Unsatisfiable for theBenchmark.p
% 116.32/86.01 % SZS output start CNFRefutation
% See solution above
% 118.62/88.24 % Total time : 85.580s
%------------------------------------------------------------------------------