%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD013-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:22:40 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 53 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(sum_8,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_8) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(not_sum_9,negated_conjecture,
~ sum(d,b,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_9) ).
cnf(sum_6,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
cnf(sum_7,negated_conjecture,
sum(additive_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(c_0_9,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_10,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_11,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_12,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_9 ).
cnf(c_0_13,negated_conjecture,
sum(a,c,u),
sum_8 ).
cnf(c_0_14,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_10 ).
cnf(c_0_15,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_11 ).
cnf(c_0_16,negated_conjecture,
sum(c,a,u),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_19,negated_conjecture,
~ sum(d,b,u),
inference(fof_simplification,[status(thm)],[not_sum_9]) ).
cnf(c_0_20,negated_conjecture,
( ~ sum(X1,X3,c)
| ~ sum(X3,a,X2)
| sum(X1,X2,u) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
sum(additive_identity,a,b),
sum_6 ).
cnf(c_0_22,plain,
( ~ sum(additive_identity,X2,X1)
| ~ defined(X2)
| sum(additive_identity,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
sum(additive_identity,c,d),
sum_7 ).
cnf(c_0_24,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_25,negated_conjecture,
~ sum(d,b,u),
c_0_19 ).
cnf(c_0_26,negated_conjecture,
( ~ sum(X1,additive_identity,c)
| sum(X1,b,u) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
sum(additive_identity,d,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
~ sum(d,additive_identity,c),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD013-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.36 % Computer : n007.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 15:35:20 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % new_bool_3 with pid 1438689 completed with status 0
% 0.12/0.43 % Result found by new_bool_3
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FHUNF-FFSM00-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 1438693 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FHUNF-FFSM00-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 35
% 0.12/0.43 % Removed by relevancy pruning/SinE : 21
% 0.12/0.43 % Initial clauses : 14
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 14
% 0.12/0.43 % Processed clauses : 100
% 0.12/0.43 % ...of these trivial : 0
% 0.12/0.43 % ...subsumed : 1
% 0.12/0.43 % ...remaining for further processing : 99
% 0.12/0.43 % Other redundant clauses eliminated : 0
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 0
% 0.12/0.43 % Backward-rewritten : 0
% 0.12/0.43 % Generated clauses : 286
% 0.12/0.43 % ...of the previous two non-redundant : 234
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 0
% 0.12/0.43 % Paramodulations : 286
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 0
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 117
% 0.12/0.43 % ...of those cached : 96
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 99
% 0.12/0.43 % Positive orientable unit clauses : 24
% 0.12/0.43 % Positive unorientable unit clauses: 0
% 0.12/0.43 % Negative unit clauses : 2
% 0.12/0.43 % Non-unit-clauses : 73
% 0.12/0.43 % Current number of unprocessed clauses: 148
% 0.12/0.43 % ...number of literals in the above : 490
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 0
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 287
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 283
% 0.12/0.43 % Non-unit clause-clause subsumptions : 1
% 0.12/0.43 % Unit Clause-clause subsumption calls : 0
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 2
% 0.12/0.43 % BW rewrite match successes : 0
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 3954
% 0.12/0.43 % Search garbage collected termcells : 156
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.005 s
% 0.12/0.43 % System time : 0.002 s
% 0.12/0.43 % Total time : 0.007 s
% 0.12/0.43 % Maximum resident set size: 3608 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.008 s
% 0.12/0.43 % System time : 0.005 s
% 0.12/0.43 % Total time : 0.013 s
% 0.12/0.43 % Maximum resident set size: 4864 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------