%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD016-1 : 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 : 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 04:18:13 PM UTC 2026
% Result : Unsatisfiable 16.37s 10.33s
% Output : CNFRefutation 16.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of clauses : 67 ( 21 unt; 0 nHn; 67 RR)
% Number of literals : 141 ( 0 equ; 76 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 77 ( 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_b_6,negated_conjecture,
equalish(add(a,v),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_b_6) ).
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(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_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(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(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_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(add_equals_b_5,negated_conjecture,
equalish(add(a,u),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_b_5) ).
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(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(u_not_equal_to_v_7,negated_conjecture,
~ equalish(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_equal_to_v_7) ).
cnf(c_0_15,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_16,negated_conjecture,
equalish(add(a,v),b),
add_equals_b_6 ).
cnf(c_0_17,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_18,negated_conjecture,
( equalish(add(add(a,v),X1),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(add(a,v),X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_21,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_22,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_23,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_24,negated_conjecture,
( equalish(add(a,add(v,X1)),add(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),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_17,c_0_23]) ).
cnf(c_0_26,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_27,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(a,add(v,X2))) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_28,plain,
( equalish(add(X1,add(X2,X3)),add(X3,add(X1,X2)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( equalish(add(v,add(X1,a)),add(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]),c_0_21])]) ).
cnf(c_0_30,plain,
( equalish(add(add(X1,X2),X3),add(add(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(v,add(X2,a))) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
( equalish(add(add(X1,X2),X3),add(X3,add(X2,X1)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_26]) ).
cnf(c_0_33,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_34,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_35,negated_conjecture,
( equalish(add(add(a,X1),v),add(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_21]),c_0_22])]) ).
cnf(c_0_36,plain,
( equalish(additive_identity,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(add(a,X2),v)) ),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_38,plain,
( equalish(add(additive_identity,X1),add(add(X2,additive_inverse(X2)),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( equalish(add(additive_identity,v),add(b,additive_inverse(a)))
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_21]),c_0_22])]) ).
cnf(c_0_40,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_41,negated_conjecture,
equalish(add(a,u),b),
add_equals_b_5 ).
cnf(c_0_42,negated_conjecture,
equalish(add(additive_identity,v),add(b,additive_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_22])]) ).
cnf(c_0_43,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_44,negated_conjecture,
( equalish(add(add(a,u),X1),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( equalish(X1,add(b,additive_inverse(a)))
| ~ equalish(X1,add(additive_identity,v)) ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_46,plain,
( equalish(X1,add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(add(a,u),X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_44]) ).
cnf(c_0_48,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_49,negated_conjecture,
equalish(v,add(b,additive_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21])]) ).
cnf(c_0_50,negated_conjecture,
( equalish(add(a,add(u,X1)),add(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_20]),c_0_48]),c_0_22])]) ).
cnf(c_0_51,negated_conjecture,
equalish(add(b,additive_inverse(a)),v),
inference(spm,[status(thm)],[c_0_33,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( equalish(X1,add(b,X2))
| ~ defined(X2)
| ~ equalish(X1,add(a,add(u,X2))) ),
inference(spm,[status(thm)],[c_0_17,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,add(b,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_17,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( equalish(add(u,add(X1,a)),add(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_28]),c_0_22]),c_0_48])]) ).
cnf(c_0_55,negated_conjecture,
( equalish(add(u,add(additive_inverse(a),a)),v)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
equalish(add(u,add(additive_inverse(a),a)),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,add(u,add(additive_inverse(a),a))) ),
inference(spm,[status(thm)],[c_0_17,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
( equalish(add(add(a,additive_inverse(a)),u),v)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_32]),c_0_48]),c_0_22])]) ).
cnf(c_0_59,negated_conjecture,
equalish(add(add(a,additive_inverse(a)),u),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_40]),c_0_22])]) ).
cnf(c_0_60,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,add(add(a,additive_inverse(a)),u)) ),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
equalish(add(additive_identity,u),v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_38]),c_0_48]),c_0_22])]) ).
cnf(c_0_62,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
equalish(v,add(additive_identity,u)),
inference(spm,[status(thm)],[c_0_33,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
equalish(v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_48])]) ).
cnf(c_0_65,negated_conjecture,
~ equalish(u,v),
u_not_equal_to_v_7 ).
cnf(c_0_66,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_64]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD016-1 : 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
% 0.16/0.33 % Computer : n026.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 17:26:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 16.37/10.33 % Version : CSE_E---1.7
% 16.37/10.33 % Problem : theBenchmark.p
% 16.37/10.33 % SZS status Unsatisfiable for theBenchmark.p
% 16.37/10.33 % SZS output start CNFRefutation
% See solution above
% 16.47/10.40 % Total time : 7.381s
%------------------------------------------------------------------------------