%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD015-3 : 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 : n022.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 1.44s 1.77s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 17 unt; 0 nHn; 31 RR)
% Number of literals : 55 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_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(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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_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(sum_3,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
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(not_sum_4,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_9,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_10,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_11,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_12,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_14,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_15,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_17,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_18,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_inverse(b)),
sum_3 ).
cnf(c_0_19,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_20,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_21,hypothesis,
( sum(X1,a,additive_identity)
| ~ sum(additive_inverse(a),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
sum(additive_inverse(a),additive_identity,additive_inverse(b)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_25,negated_conjecture,
sum(additive_inverse(b),a,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(X1,additive_inverse(b),additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
sum(a,additive_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_28,hypothesis,
sum(a,additive_identity,b),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
~ sum(additive_identity,a,b),
not_sum_4 ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD015-3 : 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
% 0.16/0.33 % Computer : n022.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 17:26:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.44/1.77 % Version : CSE_E---1.7
% 1.44/1.77 % Problem : theBenchmark.p
% 1.44/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.44/1.77 % SZS output start CNFRefutation
% See solution above
% 1.44/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------