%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD022-1 : 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 : n024.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 04:18:15 PM UTC 2026
% Result : Unsatisfiable 54.69s 32.38s
% Output : CNFRefutation 54.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 15 unt; 0 nHn; 50 RR)
% Number of literals : 110 ( 0 equ; 62 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(add_equals_add_4,negated_conjecture,
equalish(add(a,c),add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_add_4) ).
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(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(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(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(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_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(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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_not_equal_to_b_5,negated_conjecture,
~ equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_b_5) ).
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(add(a,c),add(b,c)),
add_equals_add_4 ).
cnf(c_0_16,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_17,negated_conjecture,
( equalish(add(add(a,c),X1),add(add(b,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( equalish(X1,add(add(b,c),X2))
| ~ defined(X2)
| ~ equalish(X1,add(add(a,c),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_20,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_21,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_22,negated_conjecture,
( equalish(add(a,add(c,X1)),add(add(b,c),X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_23,negated_conjecture,
( equalish(X1,add(add(b,c),X2))
| ~ defined(X2)
| ~ equalish(X1,add(a,add(c,X2))) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_24,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_25,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_26,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_27,negated_conjecture,
( equalish(add(add(c,X1),a),add(add(b,c),X1))
| ~ defined(add(c,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).
cnf(c_0_28,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_29,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_30,plain,
( equalish(add(add(X1,additive_inverse(X1)),X2),add(additive_identity,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( equalish(add(add(c,X1),a),add(add(b,c),X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20])]) ).
cnf(c_0_32,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_33,plain,
( equalish(add(add(X1,additive_inverse(X1)),X2),X2)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( equalish(X1,add(add(b,c),X2))
| ~ defined(X2)
| ~ equalish(X1,add(add(c,X2),a)) ),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_35,plain,
( equalish(X1,add(add(X2,additive_inverse(X2)),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( equalish(a,add(add(b,c),additive_inverse(c)))
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_21]),c_0_20])]) ).
cnf(c_0_37,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_38,negated_conjecture,
equalish(a,add(add(b,c),additive_inverse(c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20])]) ).
cnf(c_0_39,negated_conjecture,
equalish(add(add(b,c),additive_inverse(c)),a),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_40,plain,
( equalish(X1,add(add(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_41,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,add(add(b,c),additive_inverse(c))) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_42,plain,
( equalish(add(add(X1,X2),X3),add(add(X3,X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_28]) ).
cnf(c_0_43,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_44,negated_conjecture,
( equalish(add(add(c,additive_inverse(c)),b),a)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_43])]) ).
cnf(c_0_45,negated_conjecture,
equalish(add(add(c,additive_inverse(c)),b),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_20])]) ).
cnf(c_0_46,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,add(add(c,additive_inverse(c)),b)) ),
inference(spm,[status(thm)],[c_0_16,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
equalish(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_35]),c_0_43]),c_0_20])]) ).
cnf(c_0_48,negated_conjecture,
~ equalish(a,b),
a_not_equal_to_b_5 ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : FLD022-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 12:26:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 54.69/32.38 % Version : CSE_E---1.7
% 54.69/32.38 % Problem : theBenchmark.p
% 54.69/32.38 % SZS status Unsatisfiable for theBenchmark.p
% 54.69/32.38 % SZS output start CNFRefutation
% See solution above
% 54.99/32.63 % Total time : 23.384s
%------------------------------------------------------------------------------