%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD059-3 : 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 : n020.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 15 unt; 4 nHn; 47 RR)
% Number of literals : 114 ( 0 equ; 66 neg)
% Maximal clause size : 5 ( 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; 0-2 aty)
% Number of variables : 86 ( 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(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(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_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(totality_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
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(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(less_or_equal_2,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ less_or_equal(additive_identity,add(a,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
cnf(c_0_12,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_13,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_12 ).
cnf(c_0_14,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_15,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_16,hypothesis,
( ~ defined(X1)
| less_or_equal(a,X1)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_18,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_15 ).
cnf(c_0_19,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_17 ).
cnf(c_0_21,hypothesis,
sum(additive_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19])]) ).
cnf(c_0_22,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_23,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_24,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_25,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_26,hypothesis,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,a,X2)
| sum(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_22 ).
cnf(c_0_28,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_23 ).
cnf(c_0_29,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_24 ).
cnf(c_0_30,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_25 ).
cnf(c_0_31,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14])]) ).
cnf(c_0_32,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_33,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_34,plain,
( ~ sum(X4,X3,X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ less_or_equal(X4,X2)
| less_or_equal(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,hypothesis,
sum(add(additive_identity,additive_identity),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_32])]) ).
cnf(c_0_36,hypothesis,
( ~ sum(X2,additive_identity,X1)
| ~ less_or_equal(X2,a)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_37,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_38,hypothesis,
( ~ defined(X1)
| ~ less_or_equal(add(additive_identity,additive_identity),X1)
| less_or_equal(a,add(X1,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_14])]) ).
cnf(c_0_39,hypothesis,
( ~ defined(X1)
| ~ less_or_equal(X1,a)
| less_or_equal(add(X1,additive_identity),a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_32])]) ).
cnf(c_0_40,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_2 ).
cnf(c_0_41,negated_conjecture,
~ less_or_equal(additive_identity,add(a,a)),
inference(fof_simplification,[status(thm)],[not_less_or_equal_3]) ).
cnf(c_0_42,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_37 ).
cnf(c_0_43,hypothesis,
less_or_equal(a,add(a,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_14]),c_0_40]),c_0_32])]) ).
cnf(c_0_44,negated_conjecture,
~ less_or_equal(additive_identity,add(a,a)),
c_0_41 ).
cnf(c_0_45,hypothesis,
( ~ less_or_equal(X1,a)
| less_or_equal(X1,add(a,a)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-3 : 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 : n020.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 15:44:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.16/0.46 % Version: 3.5.1
% 0.16/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 % Starting sh5l with 300s (1) cores
% 0.16/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3289364 completed with status 0
% 0.16/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.46 % No SInE strategy applied
% 0.16/0.46 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.16/0.46 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.46 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.16/0.46 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.46 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3289369 completed with status 0
% 0.16/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.46 % No SInE strategy applied
% 0.16/0.46 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.16/0.46 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.46 % Preprocessing time : 0.002 s
% 0.16/0.46 % Presaturation interreduction done
% 0.16/0.46
% 0.16/0.46 % Proof found!
% 0.16/0.46 % SZS status Unsatisfiable
% 0.16/0.46 % SZS output start CNFRefutation
% See solution above
% 0.16/0.46 % Parsed axioms : 29
% 0.16/0.46 % Removed by relevancy pruning/SinE : 0
% 0.16/0.46 % Initial clauses : 29
% 0.16/0.46 % Removed in clause preprocessing : 0
% 0.16/0.46 % Initial clauses in saturation : 29
% 0.16/0.46 % Processed clauses : 260
% 0.16/0.46 % ...of these trivial : 6
% 0.16/0.46 % ...subsumed : 46
% 0.16/0.46 % ...remaining for further processing : 208
% 0.16/0.46 % Other redundant clauses eliminated : 0
% 0.16/0.46 % Clauses deleted for lack of memory : 0
% 0.16/0.46 % Backward-subsumed : 6
% 0.16/0.46 % Backward-rewritten : 2
% 0.16/0.46 % Generated clauses : 687
% 0.16/0.46 % ...of the previous two non-redundant : 560
% 0.16/0.46 % ...aggressively subsumed : 0
% 0.16/0.46 % Contextual simplify-reflections : 0
% 0.16/0.46 % Paramodulations : 687
% 0.16/0.46 % Factorizations : 0
% 0.16/0.46 % NegExts : 0
% 0.16/0.46 % Equation resolutions : 0
% 0.16/0.46 % Disequality decompositions : 0
% 0.16/0.46 % Total rewrite steps : 280
% 0.16/0.46 % ...of those cached : 262
% 0.16/0.46 % Propositional unsat checks : 0
% 0.16/0.46 % Propositional check models : 0
% 0.16/0.46 % Propositional check unsatisfiable : 0
% 0.16/0.46 % Propositional clauses : 0
% 0.16/0.46 % Propositional clauses after purity: 0
% 0.16/0.46 % Propositional unsat core size : 0
% 0.16/0.46 % Propositional preprocessing time : 0.000
% 0.16/0.46 % Propositional encoding time : 0.000
% 0.16/0.46 % Propositional solver time : 0.000
% 0.16/0.46 % Success case prop preproc time : 0.000
% 0.16/0.46 % Success case prop encoding time : 0.000
% 0.16/0.46 % Success case prop solver time : 0.000
% 0.16/0.46 % Current number of processed clauses : 171
% 0.16/0.46 % Positive orientable unit clauses : 22
% 0.16/0.46 % Positive unorientable unit clauses: 0
% 0.16/0.46 % Negative unit clauses : 2
% 0.16/0.46 % Non-unit-clauses : 147
% 0.16/0.46 % Current number of unprocessed clauses: 351
% 0.16/0.46 % ...number of literals in the above : 1269
% 0.16/0.46 % Current number of archived formulas : 0
% 0.16/0.46 % Current number of archived clauses : 37
% 0.16/0.46 % Clause-clause subsumption calls (NU) : 1236
% 0.16/0.46 % Rec. Clause-clause subsumption calls : 1051
% 0.16/0.46 % Non-unit clause-clause subsumptions : 52
% 0.16/0.46 % Unit Clause-clause subsumption calls : 277
% 0.16/0.46 % Rewrite failures with RHS unbound : 0
% 0.16/0.46 % BW rewrite match attempts : 6
% 0.16/0.46 % BW rewrite match successes : 2
% 0.16/0.46 % Condensation attempts : 0
% 0.16/0.46 % Condensation successes : 0
% 0.16/0.46 % Termbank termtop insertions : 10559
% 0.16/0.46 % Search garbage collected termcells : 116
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.020 s
% 0.16/0.46 % System time : 0.007 s
% 0.16/0.46 % Total time : 0.026 s
% 0.16/0.46 % Maximum resident set size: 3660 pages
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.110 s
% 0.16/0.46 % System time : 0.018 s
% 0.16/0.46 % Total time : 0.128 s
% 0.16/0.46 % Maximum resident set size: 4864 pages
% 0.16/0.46 % E exiting
%------------------------------------------------------------------------------