%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD043-3 : 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 : n025.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 04:18:21 PM UTC 2026
% Result : Unsatisfiable 38.84s 22.36s
% Output : CNFRefutation 38.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 98 ( 39 unt; 4 nHn; 98 RR)
% Number of literals : 200 ( 0 equ; 103 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 132 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(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(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(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(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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(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(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(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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(product_3,negated_conjecture,
product(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_3) ).
cnf(c_0_18,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_19,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_20,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_4 ).
cnf(c_0_21,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_22,hypothesis,
defined(multiplicative_inverse(b)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_24,hypothesis,
sum(additive_inverse(multiplicative_inverse(b)),multiplicative_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_26,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 ).
cnf(c_0_27,hypothesis,
sum(multiplicative_inverse(b),additive_inverse(multiplicative_inverse(b)),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_29,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_30,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_31,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_32,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,multiplicative_inverse(b))
| ~ sum(X2,additive_inverse(multiplicative_inverse(b)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_35,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_36,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,hypothesis,
( less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_38,hypothesis,
less_or_equal(multiplicative_inverse(b),multiplicative_inverse(b)),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_39,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_40,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_41,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_42,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_43,hypothesis,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_44,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_45,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_46,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_48,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_49,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_50,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,hypothesis,
( sum(X1,a,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_52,plain,
( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_35]),c_0_43])]) ).
cnf(c_0_54,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_55,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_56,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_57,hypothesis,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_58,plain,
( sum(X1,X2,additive_inverse(additive_identity))
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_59,hypothesis,
( sum(a,X1,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_51]) ).
cnf(c_0_60,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
cnf(c_0_61,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_62,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_63,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(additive_identity))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_64,hypothesis,
( sum(X1,b,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_65,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(b))
| ~ sum(X3,b,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_55]) ).
cnf(c_0_66,hypothesis,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_36,c_0_19]) ).
cnf(c_0_67,hypothesis,
( sum(b,X1,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_68,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_69,hypothesis,
sum(additive_inverse(a),additive_identity,additive_inverse(a)),
inference(spm,[status(thm)],[c_0_23,c_0_57]) ).
cnf(c_0_70,hypothesis,
( sum(X1,a,additive_inverse(additive_identity))
| ~ sum(X1,a,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_71,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_61]) ).
cnf(c_0_72,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_62]) ).
cnf(c_0_73,plain,
( sum(additive_inverse(additive_identity),X1,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_74,plain,
( sum(X1,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_75,hypothesis,
( sum(b,X1,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_64]) ).
cnf(c_0_76,hypothesis,
( sum(additive_identity,X1,additive_identity)
| ~ sum(additive_inverse(b),b,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,hypothesis,
( sum(X1,b,b)
| ~ sum(b,additive_identity,additive_identity)
| ~ sum(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_67]) ).
cnf(c_0_78,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
distributivity_1 ).
cnf(c_0_79,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_68,c_0_34]) ).
cnf(c_0_80,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X3,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_69]) ).
cnf(c_0_81,hypothesis,
( sum(a,X1,additive_inverse(additive_identity))
| ~ sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_70]) ).
cnf(c_0_82,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_71]) ).
cnf(c_0_83,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_84,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(additive_inverse(additive_identity),additive_inverse(additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_60])]) ).
cnf(c_0_85,hypothesis,
( sum(X1,additive_inverse(additive_identity),b)
| ~ sum(b,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_60])]) ).
cnf(c_0_86,hypothesis,
~ sum(b,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_55])]),c_0_20]) ).
cnf(c_0_87,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X4,a,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_89,hypothesis,
( sum(X1,additive_identity,additive_inverse(additive_identity))
| ~ sum(a,additive_inverse(a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_61])]) ).
cnf(c_0_90,hypothesis,
( sum(X1,additive_inverse(a),b)
| ~ sum(b,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_67]),c_0_83])]) ).
cnf(c_0_91,hypothesis,
~ sum(b,additive_identity,additive_inverse(additive_identity)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_92,hypothesis,
( sum(X1,a,a)
| ~ product(X2,a,X1)
| ~ sum(X2,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_79]) ).
cnf(c_0_93,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_88]) ).
cnf(c_0_94,hypothesis,
~ sum(b,a,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_95,hypothesis,
( sum(X1,a,a)
| ~ product(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
product(additive_identity,a,b),
product_3 ).
cnf(c_0_97,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : FLD043-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.11/0.13 % 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 : n025.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 17:28:43 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 38.84/22.36 % Version : CSE_E---1.7
% 38.84/22.36 % Problem : theBenchmark.p
% 38.84/22.36 % SZS status Unsatisfiable for theBenchmark.p
% 38.84/22.36 % SZS output start CNFRefutation
% See solution above
% 38.94/22.49 % Total time : 17.403s
%------------------------------------------------------------------------------