%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD006-1 : 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 : n017.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 04:18:10 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 7 unt; 0 nHn; 19 RR)
% Number of literals : 34 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(additive_inverse_not_equal_to_additive_identity_1,negated_conjecture,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_1) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(c_0_7,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_8,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_9,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_10,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_11,negated_conjecture,
~ equalish(additive_inverse(additive_identity),additive_identity),
additive_inverse_not_equal_to_additive_identity_1 ).
cnf(c_0_12,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( equalish(additive_identity,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_15,negated_conjecture,
~ equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,plain,
~ defined(additive_inverse(additive_identity)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_17,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_18,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD006-1 : 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
% 0.17/0.34 % Computer : n017.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 17:24:43 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------