%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD049-4 : 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 : n006.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 04:18:23 PM UTC 2026
% Result : Unsatisfiable 1.36s 1.95s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 33 unt; 3 nHn; 58 RR)
% Number of literals : 107 ( 0 equ; 52 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_10,negated_conjecture,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_10) ).
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(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(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(s_is_defined,hypothesis,
defined(s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_is_defined) ).
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(not_sum_8,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_8) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(product_11,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_11) ).
cnf(product_9,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_9) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_product_12,negated_conjecture,
~ product(b,c,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_12) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
cnf(c_0_18,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_19,negated_conjecture,
product(c,multiplicative_inverse(d),s),
product_10 ).
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,negated_conjecture,
product(multiplicative_inverse(d),c,s),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_23,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_24,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,multiplicative_inverse(d),X1)
| ~ product(X3,s,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_26,hypothesis,
defined(s),
s_is_defined ).
cnf(c_0_27,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_28,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_30,negated_conjecture,
( product(X1,c,multiply(X2,s))
| ~ product(X2,multiplicative_inverse(d),X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_32,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_33,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
not_sum_8 ).
cnf(c_0_34,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_28,c_0_23]),c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
product(multiplicative_identity,c,multiply(d,s)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_36,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_37,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_25]) ).
cnf(c_0_38,negated_conjecture,
product(multiplicative_identity,multiply(d,s),c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
product(a,d,k),
product_11 ).
cnf(c_0_40,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_9 ).
cnf(c_0_41,negated_conjecture,
( product(X1,s,c)
| ~ product(multiplicative_identity,d,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_26]),c_0_32])]) ).
cnf(c_0_42,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,d,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( product(X1,multiplicative_inverse(b),X2)
| ~ product(X3,s,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
product(d,s,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_23]),c_0_32])]) ).
cnf(c_0_45,negated_conjecture,
( product(X1,k,k)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_46,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_47,negated_conjecture,
( product(X1,multiplicative_inverse(b),c)
| ~ product(d,a,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
product(d,a,k),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
product(multiplicative_identity,k,k),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_23]),c_0_46])]) ).
cnf(c_0_50,negated_conjecture,
product(k,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,k,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
product(multiplicative_inverse(b),k,c),
inference(spm,[status(thm)],[c_0_18,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( product(X1,c,k)
| ~ product(X1,multiplicative_inverse(b),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_55,negated_conjecture,
~ product(b,c,k),
not_product_12 ).
cnf(c_0_56,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_7 ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_31]),c_0_54])]),c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.25 % Problem : FLD049-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.03/0.25 % 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
% 0.14/0.44 % Computer : n006.cluster.edu
% 0.14/0.44 % Model : x86_64 x86_64
% 0.14/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.44 % Memory : 8042.1875MB
% 0.14/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.44 % CPULimit : 300
% 0.14/0.44 % WCLimit : 300
% 0.14/0.44 % DateTime : Mon May 4 17:29:01 EDT 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 1.36/1.95 % Version : CSE_E---1.7
% 1.36/1.95 % Problem : theBenchmark.p
% 1.36/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 1.36/1.95 % SZS output start CNFRefutation
% See solution above
% 1.36/1.95 % Total time : 1.384s
%------------------------------------------------------------------------------