%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD062-3 : 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 : n031.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 04:18:27 PM UTC 2026
% Result : Unsatisfiable 6.04s 4.40s
% Output : CNFRefutation 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 17 unt; 0 nHn; 40 RR)
% Number of literals : 79 ( 0 equ; 43 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
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(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(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(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(c_0_11,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_12,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_13,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_14,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_15,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_16,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_19,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_20,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,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_23,hypothesis,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_24,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
sum(additive_inverse(b),additive_identity,additive_inverse(b)),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_26,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_27,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_28,hypothesis,
( less_or_equal(X1,additive_inverse(a))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,hypothesis,
( sum(X1,additive_inverse(a),additive_inverse(b))
| ~ sum(additive_inverse(b),a,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
~ less_or_equal(additive_inverse(b),additive_inverse(a)),
not_less_or_equal_4 ).
cnf(c_0_31,plain,
( sum(X1,additive_inverse(X2),add(X1,additive_inverse(X2)))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_32,hypothesis,
sum(b,additive_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_33,hypothesis,
( ~ less_or_equal(X1,additive_identity)
| ~ sum(additive_inverse(b),a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,plain,
( sum(additive_inverse(X1),X2,add(X2,additive_inverse(X1)))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_35,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,b)
| ~ sum(X2,additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_36,hypothesis,
~ less_or_equal(add(a,additive_inverse(b)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_12]),c_0_18])]) ).
cnf(c_0_37,hypothesis,
( less_or_equal(add(X1,additive_inverse(b)),additive_identity)
| ~ less_or_equal(X1,b)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
less_or_equal(a,b),
less_or_equal_3 ).
cnf(c_0_39,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD062-3 : 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
% 0.16/0.32 % Computer : n031.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 17:32:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.04/4.40 % Version : CSE_E---1.7
% 6.04/4.40 % Problem : theBenchmark.p
% 6.04/4.40 % SZS status Unsatisfiable for theBenchmark.p
% 6.04/4.40 % SZS output start CNFRefutation
% See solution above
% 6.04/4.41 % Total time : 3.371s
%------------------------------------------------------------------------------