%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD028-3 : 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 : n009.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 04:18:17 PM UTC 2026
% Result : Unsatisfiable 3.78s 3.14s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 20 unt; 3 nHn; 35 RR)
% Number of literals : 67 ( 0 equ; 33 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 47 ( 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/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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_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/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
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(product_7,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(product_6,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).
cnf(c_0_13,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_14,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_15,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_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_13,c_0_14]) ).
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,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_19,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,plain,
( product(multiplicative_inverse(X1),X2,X3)
| sum(additive_identity,X1,additive_identity)
| ~ product(X1,X3,X2)
| ~ defined(X3)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
product(a,v,b),
product_7 ).
cnf(c_0_22,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_23,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_24,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_5 ).
cnf(c_0_25,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1)
| ~ defined(X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
product(multiplicative_inverse(a),b,v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_28,negated_conjecture,
product(a,u,b),
product_6 ).
cnf(c_0_29,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_30,negated_conjecture,
( product(X1,multiplicative_identity,v)
| ~ product(multiplicative_inverse(a),b,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_31,negated_conjecture,
product(multiplicative_inverse(a),b,u),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_28]),c_0_29]),c_0_23])]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
product(u,multiplicative_identity,v),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
~ product(multiplicative_identity,u,v),
not_product_8 ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD028-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n009.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:27:11 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.78/3.14 % Version : CSE_E---1.7
% 3.78/3.14 % Problem : theBenchmark.p
% 3.78/3.14 % SZS status Unsatisfiable for theBenchmark.p
% 3.78/3.14 % SZS output start CNFRefutation
% See solution above
% 3.78/3.15 % Total time : 2.371s
%------------------------------------------------------------------------------