%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD066-3 : 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 : n011.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 04:18:28 PM UTC 2026
% Result : Unsatisfiable 2.38s 2.03s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 56 ( 27 unt; 3 nHn; 56 RR)
% Number of literals : 116 ( 0 equ; 59 neg)
% Maximal clause size : 4 ( 2 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 : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(sum_6,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(sum_7,negated_conjecture,
sum(b,c,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_less_or_equal_9,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_9) ).
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(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(less_or_equal_8,negated_conjecture,
less_or_equal(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_8) ).
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_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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(c_0_16,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_17,negated_conjecture,
sum(a,c,u),
sum_6 ).
cnf(c_0_18,negated_conjecture,
( less_or_equal(X1,u)
| ~ less_or_equal(X2,a)
| ~ sum(X2,c,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_20,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_21,negated_conjecture,
( less_or_equal(a,X1)
| less_or_equal(X2,u)
| ~ defined(X1)
| ~ sum(X1,c,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_22,negated_conjecture,
sum(b,c,v),
sum_7 ).
cnf(c_0_23,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_24,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_9 ).
cnf(c_0_25,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_26,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_27,negated_conjecture,
less_or_equal(v,u),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
less_or_equal(u,v),
less_or_equal_8 ).
cnf(c_0_29,negated_conjecture,
( sum(X1,c,X2)
| ~ sum(X3,u,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_30,negated_conjecture,
sum(additive_identity,u,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_32,negated_conjecture,
( sum(X1,c,v)
| ~ sum(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
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,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_35,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_19]) ).
cnf(c_0_36,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_37,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_38,negated_conjecture,
sum(a,c,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_20])]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_41,plain,
( less_or_equal(X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_43,negated_conjecture,
sum(c,a,v),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ defined(X3)
| ~ defined(X1)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
sum(c,b,v),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_46,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_47,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36])]) ).
cnf(c_0_48,negated_conjecture,
( sum(X1,a,X2)
| ~ sum(X3,v,X2)
| ~ sum(X3,c,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
sum(additive_inverse(c),v,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23]),c_0_46])]) ).
cnf(c_0_50,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_47])]) ).
cnf(c_0_51,negated_conjecture,
( sum(X1,a,b)
| ~ sum(additive_inverse(c),c,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
sum(additive_identity,a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_46])]) ).
cnf(c_0_54,negated_conjecture,
sum(additive_identity,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_20])]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_54]),c_0_23])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD066-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n011.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:30:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.38/2.03 % Version : CSE_E---1.7
% 2.38/2.03 % Problem : theBenchmark.p
% 2.38/2.03 % SZS status Unsatisfiable for theBenchmark.p
% 2.38/2.03 % SZS output start CNFRefutation
% See solution above
% 2.38/2.04 % Total time : 1.370s
%------------------------------------------------------------------------------