%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD059-2 : 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 : n020.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 04:18:26 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 15 unt; 2 nHn; 33 RR)
% Number of literals : 62 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(add_equals_u_4,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_4) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
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/FLD001-0.ax',totality_of_order_relation) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
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/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/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
cnf(c_0_11,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_12,negated_conjecture,
equalish(add(a,a),u),
add_equals_u_4 ).
cnf(c_0_13,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_14,negated_conjecture,
equalish(u,add(a,a)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_16,negated_conjecture,
( less_or_equal(add(a,a),X1)
| ~ less_or_equal(u,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_18,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_19,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_20,negated_conjecture,
less_or_equal(add(a,a),u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,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_22,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_3 ).
cnf(c_0_23,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_24,negated_conjecture,
( less_or_equal(X1,u)
| ~ less_or_equal(X1,add(a,a)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( less_or_equal(add(additive_identity,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_27,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(add(additive_identity,X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
less_or_equal(add(additive_identity,a),u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
less_or_equal(a,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
( less_or_equal(X1,u)
| ~ less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
~ less_or_equal(additive_identity,u),
not_less_or_equal_5 ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD059-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n020.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 17:30:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.75 % Version : CSE_E---1.7
% 1.33/1.75 % Problem : theBenchmark.p
% 1.33/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.75 % SZS output start CNFRefutation
% See solution above
% 1.33/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------