%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD025-3 : 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 : 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 04:18:16 PM UTC 2026
% Result : Unsatisfiable 1.95s 1.92s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 65 ( 36 unt; 0 nHn; 65 RR)
% Number of literals : 122 ( 0 equ; 59 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
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_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_5,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
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(product_6,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_product_7,negated_conjecture,
~ product(d,b,multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_7) ).
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,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_16,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_15]) ).
cnf(c_0_17,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_18,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_19,negated_conjecture,
product(multiplicative_identity,a,b),
product_5 ).
cnf(c_0_20,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_21,plain,
( product(multiplicative_identity,X1,X2)
| ~ product(multiplicative_identity,X2,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17])]) ).
cnf(c_0_22,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_23,negated_conjecture,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( product(X1,a,X2)
| ~ product(X3,b,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
product(multiplicative_identity,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( product(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( product(X1,a,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_29,negated_conjecture,
( product(X1,b,b)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_31,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),b,b),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1)
| ~ defined(X2)
| ~ defined(X5) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
product(b,multiply(multiplicative_identity,multiplicative_identity),b),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( product(X1,multiplicative_identity,b)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17])]) ).
cnf(c_0_35,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_36,negated_conjecture,
product(multiply(b,multiplicative_identity),multiplicative_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_17]),c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
product(multiplicative_identity,multiply(b,multiplicative_identity),b),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( product(multiplicative_identity,b,multiply(b,multiplicative_identity))
| ~ defined(multiply(b,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_39,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_40,plain,
( product(X1,X2,X3)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X4,X2,X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_41,negated_conjecture,
product(b,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_42,negated_conjecture,
product(multiplicative_identity,b,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_17]),c_0_35])]) ).
cnf(c_0_43,negated_conjecture,
( product(a,X1,X2)
| ~ product(b,X1,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
product(b,multiplicative_identity,multiply(b,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
product(a,multiplicative_identity,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]) ).
cnf(c_0_46,negated_conjecture,
product(multiplicative_identity,a,multiply(b,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
product(multiplicative_identity,multiply(b,multiplicative_identity),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_46]),c_0_22])]) ).
cnf(c_0_48,negated_conjecture,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_17]),c_0_35])]) ).
cnf(c_0_49,negated_conjecture,
product(multiplicative_identity,c,d),
product_6 ).
cnf(c_0_50,negated_conjecture,
product(multiply(multiplicative_identity,b),multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_35]),c_0_17])]) ).
cnf(c_0_51,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,d,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_49]) ).
cnf(c_0_52,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_53,negated_conjecture,
product(multiplicative_identity,multiply(multiplicative_identity,b),a),
inference(spm,[status(thm)],[c_0_18,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( product(X1,c,d)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_15]),c_0_52])]) ).
cnf(c_0_55,negated_conjecture,
( product(X1,b,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_35]),c_0_17])]) ).
cnf(c_0_56,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3)
| ~ defined(X4)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_57,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),c,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_17])]) ).
cnf(c_0_58,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_59,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_17])]) ).
cnf(c_0_60,negated_conjecture,
( product(X1,d,multiply(X2,c))
| ~ product(X1,multiply(multiplicative_identity,multiplicative_identity),X2)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_61,negated_conjecture,
product(b,multiply(multiplicative_identity,multiplicative_identity),a),
inference(spm,[status(thm)],[c_0_18,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
product(b,d,multiply(a,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_22])]) ).
cnf(c_0_63,negated_conjecture,
~ product(d,b,multiply(a,c)),
not_product_7 ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD025-3 : 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
% 0.16/0.33 % 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 17:27:32 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.95/1.92 % Version : CSE_E---1.7
% 1.95/1.92 % Problem : theBenchmark.p
% 1.95/1.92 % SZS status Unsatisfiable for theBenchmark.p
% 1.95/1.92 % SZS output start CNFRefutation
% See solution above
% 1.95/1.92 % Total time : 1.371s
%------------------------------------------------------------------------------