%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD064-1 : 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 : n026.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 4.68s 3.42s
% Output : CNFRefutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 19 unt; 4 nHn; 55 RR)
% Number of literals : 109 ( 0 equ; 52 neg)
% Maximal clause size : 4 ( 1 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 : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
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(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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
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(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(not_less_or_equal_3,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
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(less_or_equal_2,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
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(c_0_13,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_14,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_15,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_16,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_17,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_22,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_24,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_25,hypothesis,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_27,plain,
( less_or_equal(X1,additive_inverse(X2))
| less_or_equal(additive_inverse(X2),X1)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_28,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(a,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( equalish(add(X1,additive_inverse(X2)),add(additive_inverse(X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_30,plain,
( less_or_equal(additive_inverse(X1),additive_identity)
| less_or_equal(additive_identity,additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
not_less_or_equal_3 ).
cnf(c_0_32,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_33,hypothesis,
less_or_equal(add(additive_inverse(a),a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19])]) ).
cnf(c_0_34,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_35,hypothesis,
less_or_equal(additive_identity,additive_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_36,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,add(additive_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,hypothesis,
( less_or_equal(add(additive_identity,X1),add(additive_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_2 ).
cnf(c_0_39,hypothesis,
less_or_equal(add(additive_identity,a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19])]) ).
cnf(c_0_40,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_41,negated_conjecture,
( less_or_equal(X1,a)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_38]) ).
cnf(c_0_42,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_identity,a),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_43,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_44,negated_conjecture,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( less_or_equal(add(additive_identity,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_46,hypothesis,
less_or_equal(a,additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_48,negated_conjecture,
( less_or_equal(add(additive_identity,additive_inverse(X1)),add(a,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_23]) ).
cnf(c_0_49,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_50,hypothesis,
less_or_equal(add(additive_identity,additive_inverse(a)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_19])]) ).
cnf(c_0_51,hypothesis,
less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_identity,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_51]) ).
cnf(c_0_53,plain,
( equalish(add(additive_identity,additive_inverse(X1)),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_19])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : FLD064-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 17:31:08 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 4.68/3.42 % Version : CSE_E---1.7
% 4.68/3.42 % Problem : theBenchmark.p
% 4.68/3.42 % SZS status Unsatisfiable for theBenchmark.p
% 4.68/3.42 % SZS output start CNFRefutation
% See solution above
% 4.68/3.44 % Total time : 2.369s
%------------------------------------------------------------------------------