%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD010-5 : 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 : n016.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 9.69s 6.33s
% Output : CNFRefutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of clauses : 68 ( 19 unt; 8 nHn; 68 RR)
% Number of literals : 166 ( 0 equ; 96 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 : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 136 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(not_sum_1,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
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(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(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_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
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(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(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(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(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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(not_sum_2,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
cnf(c_0_17,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_18,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_19,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
not_sum_1 ).
cnf(c_0_20,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_21,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_22,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_24,plain,
( less_or_equal(multiplicative_identity,X1)
| less_or_equal(X1,multiplicative_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,plain,
( product(X1,X2,multiplicative_identity)
| ~ product(X1,X3,multiplicative_inverse(multiplicative_identity))
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_27,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_19]) ).
cnf(c_0_28,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_29,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_30,plain,
less_or_equal(multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_24]),c_0_18])]) ).
cnf(c_0_31,plain,
( product(multiplicative_identity,X1,multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,plain,
( less_or_equal(additive_identity,X1)
| less_or_equal(X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_33,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_34,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30])]) ).
cnf(c_0_35,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_36,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_32]),c_0_28])]) ).
cnf(c_0_37,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_39,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_40,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_41,plain,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_42,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_43,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_36])]) ).
cnf(c_0_44,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_45,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18])]) ).
cnf(c_0_46,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_47,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_48,plain,
( product(X1,X2,multiplicative_identity)
| ~ product(X1,X3,multiplicative_identity)
| ~ product(multiplicative_identity,X3,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_49,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( sum(multiplicative_identity,X1,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,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_52,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X2,multiplicative_identity,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
( product(multiplicative_inverse(multiplicative_identity),X1,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_22]) ).
cnf(c_0_54,plain,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_43])]) ).
cnf(c_0_55,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ defined(X3)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_51,c_0_26]) ).
cnf(c_0_56,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_27]),c_0_35])]) ).
cnf(c_0_57,plain,
( sum(additive_identity,X1,multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_54]) ).
cnf(c_0_58,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_59,plain,
( sum(X1,X2,X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(additive_identity,X3,X1)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_34]) ).
cnf(c_0_60,plain,
( product(X1,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
not_sum_2 ).
cnf(c_0_62,plain,
( sum(additive_identity,X1,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_63,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_64,plain,
( sum(X1,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_18]),c_0_35])]) ).
cnf(c_0_65,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_27])]),c_0_65]) ).
cnf(c_0_67,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_47]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD010-5 : 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
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:27:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 9.69/6.33 % Version : CSE_E---1.7
% 9.69/6.33 % Problem : theBenchmark.p
% 9.69/6.33 % SZS status Unsatisfiable for theBenchmark.p
% 9.69/6.33 % SZS output start CNFRefutation
% See solution above
% 9.69/6.37 % Total time : 4.368s
%------------------------------------------------------------------------------