%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD064-3 : 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 : n012.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 12:22:55 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.35s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 8 unt; 0 nHn; 27 RR)
% Number of literals : 55 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 39 ( 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(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
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(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
cnf(less_or_equal_2,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_0_8,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_9,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_10,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_11,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_8 ).
cnf(c_0_12,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_9 ).
cnf(c_0_13,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_14,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_15,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_10 ).
cnf(c_0_16,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_13 ).
cnf(c_0_18,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_14 ).
cnf(c_0_19,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(fof_simplification,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_0_20,plain,
( ~ sum(X2,additive_inverse(X3),X1)
| ~ defined(X3)
| ~ less_or_equal(X2,X3)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ defined(X1)
| sum(additive_identity,additive_inverse(X1),additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
c_0_19 ).
cnf(c_0_23,plain,
( ~ defined(X1)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_2 ).
cnf(c_0_25,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 15:43:54 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.35 % Version: 3.5.1
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.35 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.35 % Starting sh5l with 300s (1) cores
% 0.07/0.35 % new_bool_3 with pid 2679517 completed with status 0
% 0.07/0.35 % Result found by new_bool_3
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.35 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.35 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.35 % Search class: FGUNF-FFMS11-SFFFFFNN
% 0.07/0.35 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.35 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.35 % SubtermCWHack with pid 2679522 completed with status 0
% 0.07/0.35 % Result found by SubtermCWHack
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.35 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.35 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.35 % Search class: FGUNF-FFMS11-SFFFFFNN
% 0.07/0.35 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.35 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.35 % Preprocessing time : 0.001 s
% 0.07/0.35
% 0.07/0.35 % Proof found!
% 0.07/0.35 % SZS status Unsatisfiable
% 0.07/0.35 % SZS output start CNFRefutation
% See solution above
% 0.07/0.35 % Parsed axioms : 29
% 0.07/0.35 % Removed by relevancy pruning/SinE : 9
% 0.07/0.35 % Initial clauses : 20
% 0.07/0.35 % Removed in clause preprocessing : 0
% 0.07/0.35 % Initial clauses in saturation : 20
% 0.07/0.35 % Processed clauses : 186
% 0.07/0.35 % ...of these trivial : 5
% 0.07/0.35 % ...subsumed : 75
% 0.07/0.35 % ...remaining for further processing : 106
% 0.07/0.35 % Other redundant clauses eliminated : 0
% 0.07/0.35 % Clauses deleted for lack of memory : 0
% 0.07/0.35 % Backward-subsumed : 0
% 0.07/0.35 % Backward-rewritten : 2
% 0.07/0.35 % Generated clauses : 556
% 0.07/0.35 % ...of the previous two non-redundant : 330
% 0.07/0.35 % ...aggressively subsumed : 0
% 0.07/0.35 % Contextual simplify-reflections : 0
% 0.07/0.35 % Paramodulations : 556
% 0.07/0.35 % Factorizations : 0
% 0.07/0.35 % NegExts : 0
% 0.07/0.35 % Equation resolutions : 0
% 0.07/0.35 % Disequality decompositions : 0
% 0.07/0.35 % Total rewrite steps : 422
% 0.07/0.35 % ...of those cached : 404
% 0.07/0.35 % Propositional unsat checks : 0
% 0.07/0.35 % Propositional check models : 0
% 0.07/0.35 % Propositional check unsatisfiable : 0
% 0.07/0.35 % Propositional clauses : 0
% 0.07/0.35 % Propositional clauses after purity: 0
% 0.07/0.35 % Propositional unsat core size : 0
% 0.07/0.35 % Propositional preprocessing time : 0.000
% 0.07/0.35 % Propositional encoding time : 0.000
% 0.07/0.35 % Propositional solver time : 0.000
% 0.07/0.35 % Success case prop preproc time : 0.000
% 0.07/0.35 % Success case prop encoding time : 0.000
% 0.07/0.35 % Success case prop solver time : 0.000
% 0.07/0.35 % Current number of processed clauses : 104
% 0.07/0.35 % Positive orientable unit clauses : 19
% 0.07/0.35 % Positive unorientable unit clauses: 0
% 0.07/0.35 % Negative unit clauses : 3
% 0.07/0.35 % Non-unit-clauses : 82
% 0.07/0.35 % Current number of unprocessed clauses: 152
% 0.07/0.35 % ...number of literals in the above : 511
% 0.07/0.35 % Current number of archived formulas : 0
% 0.07/0.35 % Current number of archived clauses : 2
% 0.07/0.35 % Clause-clause subsumption calls (NU) : 431
% 0.07/0.35 % Rec. Clause-clause subsumption calls : 397
% 0.07/0.35 % Non-unit clause-clause subsumptions : 44
% 0.07/0.35 % Unit Clause-clause subsumption calls : 16
% 0.07/0.35 % Rewrite failures with RHS unbound : 0
% 0.07/0.35 % BW rewrite match attempts : 12
% 0.07/0.35 % BW rewrite match successes : 2
% 0.07/0.35 % Condensation attempts : 0
% 0.07/0.35 % Condensation successes : 0
% 0.07/0.35 % Termbank termtop insertions : 8188
% 0.07/0.35 % Search garbage collected termcells : 140
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.009 s
% 0.07/0.35 % System time : 0.000 s
% 0.07/0.35 % Total time : 0.009 s
% 0.07/0.35 % Maximum resident set size: 3660 pages
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.010 s
% 0.07/0.35 % System time : 0.003 s
% 0.07/0.35 % Total time : 0.013 s
% 0.07/0.35 % Maximum resident set size: 4608 pages
% 0.07/0.35 % E exiting
%------------------------------------------------------------------------------