%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD065-1 : 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 : n014.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 5.96s 4.44s
% Output : CNFRefutation 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 70 ( 22 unt; 2 nHn; 70 RR)
% Number of literals : 142 ( 0 equ; 72 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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/FLD001-0.ax',totality_of_order_relation) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_inverse_addition,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(less_or_equal_2,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
cnf(c_0_16,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_17,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_18,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_19,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_20,hypothesis,
( equalish(add(X1,a),add(a,X1))
| ~ 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,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_18]) ).
cnf(c_0_23,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_24,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_25,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_26,hypothesis,
equalish(add(additive_identity,a),add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_28,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_29,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_30,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
equalish(add(a,additive_identity),add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_33,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_34,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_35,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
equalish(add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_38,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_39,hypothesis,
( equalish(add(add(additive_identity,a),X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_40,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ equalish(a,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
equalish(a,add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_42,hypothesis,
( less_or_equal(add(a,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_43,hypothesis,
( equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_45,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(a,additive_identity)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
less_or_equal(add(a,additive_identity),add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_47,hypothesis,
equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]) ).
cnf(c_0_48,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_49,hypothesis,
less_or_equal(add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,add(a,additive_identity))
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
less_or_equal_2 ).
cnf(c_0_52,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(add(additive_identity,a),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_53,plain,
( equalish(add(X1,add(X2,X3)),add(add(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_48]) ).
cnf(c_0_54,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(add(a,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_55,hypothesis,
( equalish(add(a,additive_identity),X1)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_56,plain,
( equalish(add(additive_identity,add(X1,X2)),add(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( less_or_equal(add(additive_inverse(a),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_58,hypothesis,
( equalish(add(additive_inverse(a),add(additive_identity,a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_17]),c_0_21])]) ).
cnf(c_0_59,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,hypothesis,
( equalish(add(additive_identity,add(X1,a)),add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_17]) ).
cnf(c_0_61,negated_conjecture,
( less_or_equal(X1,add(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(add(additive_inverse(a),X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_57]) ).
cnf(c_0_62,hypothesis,
equalish(add(additive_inverse(a),add(additive_identity,a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_44]),c_0_17])]) ).
cnf(c_0_63,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ equalish(X2,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_64,hypothesis,
equalish(add(additive_identity,add(additive_identity,a)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_21])]) ).
cnf(c_0_65,negated_conjecture,
( less_or_equal(additive_identity,add(additive_identity,add(additive_identity,a)))
| ~ defined(add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(additive_identity,add(additive_identity,a))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
less_or_equal(additive_identity,add(additive_identity,add(additive_identity,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_17]),c_0_21])]) ).
cnf(c_0_68,negated_conjecture,
~ less_or_equal(additive_identity,a),
not_less_or_equal_3 ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD065-1 : 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
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:30:52 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.96/4.44 % Version : CSE_E---1.7
% 5.96/4.44 % Problem : theBenchmark.p
% 5.96/4.44 % SZS status Unsatisfiable for theBenchmark.p
% 5.96/4.44 % SZS output start CNFRefutation
% See solution above
% 5.96/4.46 % Total time : 3.371s
%------------------------------------------------------------------------------