%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD013-2 : 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 : 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 04:18:12 PM UTC 2026
% Result : Unsatisfiable 1.56s 1.82s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 26 unt; 0 nHn; 40 RR)
% Number of literals : 63 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 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(add_equals_u_8,negated_conjecture,
equalish(add(a,c),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_8) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(c_equals_d_7,negated_conjecture,
equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_equals_d_7) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(a_equals_b_6,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_6) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(add_not_equal_to_u_9,negated_conjecture,
~ equalish(add(d,b),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_not_equal_to_u_9) ).
cnf(c_0_12,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_13,negated_conjecture,
equalish(add(a,c),u),
add_equals_u_8 ).
cnf(c_0_14,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_15,negated_conjecture,
equalish(c,d),
c_equals_d_7 ).
cnf(c_0_16,negated_conjecture,
( equalish(X1,u)
| ~ equalish(X1,add(a,c)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_18,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_19,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_20,negated_conjecture,
( equalish(add(c,X1),add(d,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_22,negated_conjecture,
equalish(add(c,a),u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
( equalish(X1,add(d,X2))
| ~ defined(X2)
| ~ equalish(X1,add(c,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
equalish(u,add(c,a)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
equalish(u,add(d,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18])]) ).
cnf(c_0_27,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_28,negated_conjecture,
equalish(u,add(a,d)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_27])]) ).
cnf(c_0_29,negated_conjecture,
equalish(a,b),
a_equals_b_6 ).
cnf(c_0_30,negated_conjecture,
equalish(add(a,d),u),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
equalish(b,a),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( equalish(X1,u)
| ~ equalish(X1,add(a,d)) ),
inference(spm,[status(thm)],[c_0_12,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( equalish(add(b,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
equalish(add(b,d),u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
equalish(u,add(b,d)),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_36,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_37,negated_conjecture,
equalish(u,add(d,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_27]),c_0_36])]) ).
cnf(c_0_38,negated_conjecture,
~ equalish(add(d,b),u),
add_not_equal_to_u_9 ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD013-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:24:57 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.56/1.82 % Version : CSE_E---1.7
% 1.56/1.82 % Problem : theBenchmark.p
% 1.56/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.56/1.82 % SZS output start CNFRefutation
% See solution above
% 1.56/1.82 % Total time : 1.371s
%------------------------------------------------------------------------------