%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD002-3 : 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 : 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 04:18:09 PM UTC 2026
% Result : Unsatisfiable 1.82s 1.88s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 26 unt; 0 nHn; 55 RR)
% Number of literals : 108 ( 0 equ; 56 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(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_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
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_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(product_3,hypothesis,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_3) ).
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(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_4,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_14,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_15,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_16,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_17,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_18,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_19,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( sum(X1,b,add(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_22,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_23,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
sum(additive_identity,b,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_26,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_27,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
sum(b,additive_identity,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_29,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_30,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_31,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_32,hypothesis,
product(multiplicative_identity,a,b),
product_3 ).
cnf(c_0_33,hypothesis,
sum(b,additive_identity,b),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_34,hypothesis,
( sum(X1,add(additive_identity,b),a)
| ~ sum(X1,b,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,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_36,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_38,hypothesis,
( product(X1,X2,b)
| ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_40,hypothesis,
( sum(add(additive_identity,b),X1,a)
| ~ sum(X1,b,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_41,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_43,hypothesis,
( product(X1,a,b)
| ~ product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_44,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_45,hypothesis,
( sum(X1,a,b)
| ~ sum(X1,add(additive_identity,b),b)
| ~ sum(additive_identity,b,a) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,hypothesis,
( sum(X1,add(additive_identity,b),b)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_47,hypothesis,
( sum(X1,additive_identity,a)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,hypothesis,
( product(a,X1,b)
| ~ product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_49,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_50,hypothesis,
( sum(X1,a,b)
| ~ sum(additive_identity,b,a)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
~ sum(additive_identity,a,b),
not_sum_4 ).
cnf(c_0_52,hypothesis,
sum(b,additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_23]),c_0_49])]) ).
cnf(c_0_53,hypothesis,
~ sum(additive_identity,b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_26]),c_0_51]) ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD002-3 : 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
% 0.15/0.33 % Computer : n016.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 17:26:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.82/1.88 % Version : CSE_E---1.7
% 1.82/1.88 % Problem : theBenchmark.p
% 1.82/1.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.82/1.88 % SZS output start CNFRefutation
% See solution above
% 1.82/1.89 % Total time : 1.370s
%------------------------------------------------------------------------------