%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD007-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:22:38 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 8 unt; 0 nHn; 26 RR)
% Number of literals : 51 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(c_0_7,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_8,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_9,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_7 ).
cnf(c_0_10,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_11,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_8 ).
cnf(c_0_12,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_14,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,a,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_13 ).
cnf(c_0_16,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_17,hypothesis,
( ~ sum(X1,additive_inverse(a),additive_identity)
| sum(X1,additive_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_10])]) ).
cnf(c_0_18,negated_conjecture,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),a),
inference(fof_simplification,[status(thm)],[not_sum_2]) ).
cnf(c_0_19,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_16 ).
cnf(c_0_20,hypothesis,
( ~ defined(additive_inverse(a))
| sum(additive_inverse(additive_inverse(a)),additive_identity,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),a),
c_0_18 ).
cnf(c_0_22,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_23,hypothesis,
~ defined(additive_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_22 ).
cnf(c_0_25,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD007-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 15:32:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % sh5l with pid 2658989 completed with status 0
% 0.12/0.45 % Result found by sh5l
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.45 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.12/0.45 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.45 % SubtermCWHack with pid 2658996 completed with status 0
% 0.12/0.45 % Result found by SubtermCWHack
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.45 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.12/0.45 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.45 % Preprocessing time : 0.001 s
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 28
% 0.12/0.45 % Removed by relevancy pruning/SinE : 2
% 0.12/0.45 % Initial clauses : 26
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 26
% 0.12/0.45 % Processed clauses : 104
% 0.12/0.45 % ...of these trivial : 0
% 0.12/0.45 % ...subsumed : 18
% 0.12/0.45 % ...remaining for further processing : 86
% 0.12/0.45 % Other redundant clauses eliminated : 0
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 1
% 0.12/0.45 % Backward-rewritten : 0
% 0.12/0.45 % Generated clauses : 229
% 0.12/0.45 % ...of the previous two non-redundant : 170
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 0
% 0.12/0.45 % Paramodulations : 229
% 0.12/0.45 % Factorizations : 0
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 0
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 44
% 0.12/0.45 % ...of those cached : 33
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 85
% 0.12/0.45 % Positive orientable unit clauses : 13
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 3
% 0.12/0.45 % Non-unit-clauses : 69
% 0.12/0.45 % Current number of unprocessed clauses: 92
% 0.12/0.45 % ...number of literals in the above : 372
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 1
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 438
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 350
% 0.12/0.45 % Non-unit clause-clause subsumptions : 18
% 0.12/0.45 % Unit Clause-clause subsumption calls : 42
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 1
% 0.12/0.45 % BW rewrite match successes : 0
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 3930
% 0.12/0.45 % Search garbage collected termcells : 121
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.009 s
% 0.12/0.45 % System time : 0.002 s
% 0.12/0.45 % Total time : 0.011 s
% 0.12/0.45 % Maximum resident set size: 3660 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.009 s
% 0.12/0.45 % System time : 0.008 s
% 0.12/0.45 % Total time : 0.017 s
% 0.12/0.45 % Maximum resident set size: 4864 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------