%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD008-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 1.63s 1.84s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of clauses : 70 ( 26 unt; 2 nHn; 70 RR)
% Number of literals : 152 ( 0 equ; 82 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(sum_5,negated_conjecture,
sum(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_5) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(sum_6,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
cnf(c_0_16,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_17,negated_conjecture,
sum(a,b,c),
sum_5 ).
cnf(c_0_18,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_19,negated_conjecture,
( less_or_equal(X1,c)
| ~ less_or_equal(X2,a)
| ~ sum(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_18]) ).
cnf(c_0_21,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_22,negated_conjecture,
( less_or_equal(X1,c)
| ~ sum(a,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_23,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_24,negated_conjecture,
less_or_equal(c,c),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_25,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_26,negated_conjecture,
sum(additive_identity,c,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
( sum(X1,c,X2)
| ~ sum(X3,c,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_29,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_30,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_31,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_32,negated_conjecture,
( sum(X1,c,additive_identity)
| ~ sum(additive_inverse(c),additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_35,negated_conjecture,
( sum(additive_inverse(c),c,additive_identity)
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_37,negated_conjecture,
( sum(X1,b,X2)
| ~ sum(X3,c,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_38,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_39,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
sum(additive_inverse(c),c,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29])]) ).
cnf(c_0_41,negated_conjecture,
( sum(X1,b,add(X2,c))
| ~ defined(X2)
| ~ sum(X2,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29])]) ).
cnf(c_0_42,negated_conjecture,
sum(b,a,c),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_43,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_44,plain,
( sum(X1,X2,add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( sum(additive_inverse(c),X1,X2)
| ~ defined(X2)
| ~ sum(c,X2,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
sum(c,b,add(b,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_47,plain,
( sum(X1,X2,X3)
| ~ defined(X4)
| ~ defined(X2)
| ~ sum(X5,add(X2,X4),X3)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
sum(additive_inverse(c),add(b,c),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]) ).
cnf(c_0_49,negated_conjecture,
( sum(X1,b,b)
| ~ sum(additive_inverse(c),c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29]),c_0_43])]) ).
cnf(c_0_50,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
sum_6 ).
cnf(c_0_51,negated_conjecture,
sum(additive_identity,b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_28]),c_0_29])]) ).
cnf(c_0_52,negated_conjecture,
( sum(X1,X2,d)
| ~ sum(X3,additive_inverse(b),X2)
| ~ sum(X1,X3,additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( sum(X1,d,d)
| ~ sum(X1,additive_inverse(a),additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_52,c_0_50]) ).
cnf(c_0_55,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_56,negated_conjecture,
( sum(X1,c,b)
| ~ sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_53,c_0_17]) ).
cnf(c_0_57,negated_conjecture,
( sum(additive_identity,d,d)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_54,c_0_31]) ).
cnf(c_0_58,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
sum(additive_inverse(a),c,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_21])]) ).
cnf(c_0_60,negated_conjecture,
sum(additive_identity,d,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_21])]) ).
cnf(c_0_61,negated_conjecture,
( sum(X1,d,additive_identity)
| ~ sum(X1,additive_inverse(a),b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_50]),c_0_43])]) ).
cnf(c_0_62,negated_conjecture,
sum(c,additive_inverse(a),b),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_63,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ defined(X2)
| ~ sum(X4,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_64,negated_conjecture,
sum(d,additive_identity,d),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
sum(c,d,additive_identity),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( sum(X1,additive_inverse(X2),d)
| ~ defined(X2)
| ~ sum(d,X2,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
sum(d,c,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
not_sum_7 ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_29])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD008-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:26:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.63/1.84 % Version : CSE_E---1.7
% 1.63/1.84 % Problem : theBenchmark.p
% 1.63/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.84 % SZS output start CNFRefutation
% See solution above
% 1.63/1.85 % Total time : 1.371s
%------------------------------------------------------------------------------