%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD068-3 : 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 : n012.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 04:18:29 PM UTC 2026
% Result : Unsatisfiable 4.62s 4.18s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of clauses : 95 ( 36 unt; 3 nHn; 95 RR)
% Number of literals : 195 ( 0 equ; 101 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(c_0_16,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_17,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_18,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_19,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,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_21,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_23,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_24,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_25,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_26,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,a)
| ~ sum(X2,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( sum(X1,additive_inverse(X2),add(X1,additive_inverse(X2)))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
( less_or_equal(X1,b)
| less_or_equal(b,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_4 ).
cnf(c_0_30,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_31,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
less_or_equal_3 ).
cnf(c_0_32,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_33,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_34,hypothesis,
( less_or_equal(add(X1,additive_inverse(a)),additive_identity)
| ~ less_or_equal(X1,a)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]) ).
cnf(c_0_35,hypothesis,
less_or_equal(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( less_or_equal(X1,add(b,additive_inverse(a)))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( sum(additive_identity,add(b,additive_inverse(a)),additive_identity)
| ~ less_or_equal(add(b,additive_inverse(a)),additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_39,hypothesis,
less_or_equal(add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_35])]) ).
cnf(c_0_40,negated_conjecture,
( sum(additive_identity,add(b,additive_inverse(a)),X1)
| ~ less_or_equal(add(b,additive_inverse(a)),X1)
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_41,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_42,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_43,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
sum(additive_identity,add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_45,negated_conjecture,
( sum(additive_identity,add(b,additive_inverse(a)),add(b,additive_inverse(a)))
| ~ less_or_equal(add(b,additive_inverse(a)),additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_46,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_47,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_24]) ).
cnf(c_0_48,plain,
( sum(X1,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
sum(add(b,additive_inverse(a)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( sum(add(b,additive_inverse(a)),additive_identity,add(b,additive_inverse(a)))
| ~ less_or_equal(add(b,additive_inverse(a)),additive_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_51,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_41,c_0_17]) ).
cnf(c_0_52,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_43]) ).
cnf(c_0_53,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_32]) ).
cnf(c_0_54,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_47,c_0_32]) ).
cnf(c_0_55,negated_conjecture,
( sum(X1,additive_inverse(additive_identity),additive_identity)
| ~ sum(add(b,additive_inverse(a)),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
sum(add(b,additive_inverse(a)),additive_identity,add(b,additive_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_39])]) ).
cnf(c_0_57,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_58,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_59,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
sum(add(b,additive_inverse(a)),additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_62,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_53]) ).
cnf(c_0_63,hypothesis,
( sum(X1,a,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_51]) ).
cnf(c_0_64,plain,
( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_33,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_39])]) ).
cnf(c_0_66,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_67,hypothesis,
sum(b,additive_identity,b),
inference(spm,[status(thm)],[c_0_18,c_0_61]) ).
cnf(c_0_68,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_61]) ).
cnf(c_0_69,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_62]) ).
cnf(c_0_70,hypothesis,
( sum(a,X1,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_63]) ).
cnf(c_0_71,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_72,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,hypothesis,
( sum(X1,b,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_61]) ).
cnf(c_0_74,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_75,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(a,additive_inverse(additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_76,hypothesis,
( sum(X1,additive_inverse(additive_identity),b)
| ~ sum(X1,additive_identity,b) ),
inference(spm,[status(thm)],[c_0_72,c_0_71]) ).
cnf(c_0_77,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ defined(X4)
| ~ defined(X2)
| ~ sum(X5,add(X4,additive_inverse(X2)),X3)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_78,negated_conjecture,
sum(additive_inverse(additive_identity),add(b,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_60]) ).
cnf(c_0_79,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_61]) ).
cnf(c_0_80,hypothesis,
( sum(b,X1,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_73]) ).
cnf(c_0_81,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_66,c_0_74]) ).
cnf(c_0_82,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X2,b)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_67]) ).
cnf(c_0_83,hypothesis,
( sum(b,additive_identity,a)
| ~ sum(a,additive_identity,b) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_85,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_51]) ).
cnf(c_0_86,negated_conjecture,
( sum(X1,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(additive_identity),b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_25]),c_0_17])]) ).
cnf(c_0_87,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_79,c_0_61]) ).
cnf(c_0_88,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(b,additive_inverse(additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_80]),c_0_71])]) ).
cnf(c_0_89,hypothesis,
( sum(X1,additive_inverse(additive_identity),a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_81,c_0_71]) ).
cnf(c_0_90,hypothesis,
~ sum(a,additive_identity,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]),c_0_29]) ).
cnf(c_0_91,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(X1,additive_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_85,c_0_19]) ).
cnf(c_0_92,hypothesis,
sum(b,additive_inverse(a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_37])]) ).
cnf(c_0_93,hypothesis,
~ sum(b,additive_identity,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_94,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : FLD068-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.04/0.14 % 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
% 0.07/0.38 % Computer : n012.cluster.edu
% 0.07/0.38 % Model : x86_64 x86_64
% 0.07/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.38 % Memory : 8042.1875MB
% 0.07/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.38 % CPULimit : 300
% 0.07/0.38 % WCLimit : 300
% 0.07/0.38 % DateTime : Mon May 4 17:30:16 EDT 2026
% 0.07/0.38 % CPUTime :
% 0.07/0.39 % start to proof: theBenchmark
% 4.62/4.18 % Version : CSE_E---1.7
% 4.62/4.18 % Problem : theBenchmark.p
% 4.62/4.18 % SZS status Unsatisfiable for theBenchmark.p
% 4.62/4.18 % SZS output start CNFRefutation
% See solution above
% 4.71/4.20 % Total time : 3.366s
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