%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD016-5 : 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 : n008.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 2.37s 2.04s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 22 unt; 0 nHn; 40 RR)
% Number of literals : 75 ( 0 equ; 37 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(sum_6,negated_conjecture,
sum(a,u,q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(sum_8,negated_conjecture,
sum(additive_identity,q,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_8) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(sum_7,negated_conjecture,
sum(a,v,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
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(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_sum_9,negated_conjecture,
~ sum(additive_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_9) ).
cnf(c_0_12,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_13,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_14,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_15,negated_conjecture,
sum(a,u,q),
sum_6 ).
cnf(c_0_16,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_18,negated_conjecture,
( sum(X1,u,X2)
| ~ sum(X3,q,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
sum(additive_identity,q,r),
sum_8 ).
cnf(c_0_20,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_21,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ defined(X3)
| ~ defined(X1)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
sum(a,v,r),
sum_7 ).
cnf(c_0_23,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_24,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_25,negated_conjecture,
( sum(X1,u,r)
| ~ sum(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
sum(additive_inverse(a),r,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
sum(a,u,r),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_24])]) ).
cnf(c_0_29,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
sum(r,additive_inverse(a),v),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
sum(u,a,r),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_32,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_33,negated_conjecture,
( sum(X1,v,additive_identity)
| ~ sum(X1,r,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]) ).
cnf(c_0_34,negated_conjecture,
sum(additive_inverse(u),r,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_31]),c_0_24]),c_0_32])]) ).
cnf(c_0_35,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ defined(X1)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
sum(additive_inverse(u),v,additive_identity),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
sum(u,additive_identity,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23]),c_0_32])]) ).
cnf(c_0_38,negated_conjecture,
~ sum(additive_identity,u,v),
not_sum_9 ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD016-5 : 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
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:26:43 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.37/2.04 % Version : CSE_E---1.7
% 2.37/2.04 % Problem : theBenchmark.p
% 2.37/2.04 % SZS status Unsatisfiable for theBenchmark.p
% 2.37/2.04 % SZS output start CNFRefutation
% See solution above
% 2.37/2.04 % Total time : 1.369s
%------------------------------------------------------------------------------