%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD059-4 : 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 : n009.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 12:22:54 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 19 unt; 4 nHn; 38 RR)
% Number of literals : 77 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
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(transitivity_of_order_relation,axiom,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
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(sum_4,negated_conjecture,
sum(a,a,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_4) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(c_0_11,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_12,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_11 ).
cnf(c_0_13,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_14,negated_conjecture,
~ less_or_equal(additive_identity,u),
inference(fof_simplification,[status(thm)],[not_less_or_equal_5]) ).
cnf(c_0_15,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_16,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_17,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_order_relation]) ).
cnf(c_0_18,hypothesis,
( ~ defined(X1)
| less_or_equal(X1,u)
| less_or_equal(u,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_20,negated_conjecture,
~ less_or_equal(additive_identity,u),
c_0_14 ).
cnf(c_0_21,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_15 ).
cnf(c_0_22,negated_conjecture,
sum(a,a,u),
sum_4 ).
cnf(c_0_23,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_16 ).
cnf(c_0_24,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_25,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_26,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_17 ).
cnf(c_0_27,hypothesis,
less_or_equal(u,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ sum(X2,a,X1)
| ~ less_or_equal(X2,a)
| less_or_equal(X1,u) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_3 ).
cnf(c_0_31,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_25 ).
cnf(c_0_32,hypothesis,
( ~ less_or_equal(X1,u)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
less_or_equal(a,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
( ~ less_or_equal(a,additive_identity)
| sum(additive_identity,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_35,hypothesis,
less_or_equal(a,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
sum(additive_identity,a,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_30])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n009.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 15:43:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % new_bool_3 with pid 2125813 completed with status 0
% 0.12/0.44 % Result found by new_bool_3
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % SubtermCWHack with pid 2125818 completed with status 0
% 0.12/0.44 % Result found by SubtermCWHack
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.44 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.12/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 31
% 0.12/0.44 % Removed by relevancy pruning/SinE : 11
% 0.12/0.44 % Initial clauses : 20
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 20
% 0.12/0.44 % Processed clauses : 50
% 0.12/0.44 % ...of these trivial : 1
% 0.12/0.44 % ...subsumed : 5
% 0.12/0.44 % ...remaining for further processing : 44
% 0.12/0.44 % Other redundant clauses eliminated : 0
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 2
% 0.12/0.44 % Backward-rewritten : 2
% 0.12/0.44 % Generated clauses : 80
% 0.12/0.44 % ...of the previous two non-redundant : 58
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 80
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 0
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 32
% 0.12/0.44 % ...of those cached : 19
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 40
% 0.12/0.44 % Positive orientable unit clauses : 20
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 1
% 0.12/0.44 % Non-unit-clauses : 19
% 0.12/0.44 % Current number of unprocessed clauses: 25
% 0.12/0.44 % ...number of literals in the above : 72
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 4
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 23
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 22
% 0.12/0.44 % Non-unit clause-clause subsumptions : 5
% 0.12/0.44 % Unit Clause-clause subsumption calls : 5
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 9
% 0.12/0.44 % BW rewrite match successes : 3
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 1643
% 0.12/0.44 % Search garbage collected termcells : 145
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.005 s
% 0.12/0.44 % System time : 0.000 s
% 0.12/0.44 % Total time : 0.005 s
% 0.12/0.44 % Maximum resident set size: 3660 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.008 s
% 0.12/0.44 % System time : 0.004 s
% 0.12/0.44 % Total time : 0.012 s
% 0.12/0.44 % Maximum resident set size: 4608 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------