%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD059-2 : 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 : n006.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 12:22:53 PM UTC 2026
% Result : Unsatisfiable 0.23s 5.99s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 61 ( 20 unt; 4 nHn; 61 RR)
% Number of literals : 131 ( 0 equ; 70 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_equality,axiom,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(add_equals_u_4,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_u_4) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_5) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(transitivity_of_order_relation,axiom,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(c_0_15,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_equality]) ).
cnf(c_0_16,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_17,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
c_0_15 ).
cnf(c_0_18,negated_conjecture,
equalish(add(a,a),u),
add_equals_u_4 ).
cnf(c_0_19,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_addition]) ).
cnf(c_0_20,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_16 ).
cnf(c_0_21,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_22,negated_conjecture,
~ less_or_equal(additive_identity,u),
inference(fof_simplification,[status(thm)],[not_less_or_equal_5]) ).
cnf(c_0_23,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[symmetry_of_equality]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_25,negated_conjecture,
( ~ equalish(X1,add(a,a))
| equalish(X1,u) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
c_0_19 ).
cnf(c_0_27,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_28,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_29,hypothesis,
( ~ defined(X1)
| less_or_equal(X1,u)
| less_or_equal(u,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_31,negated_conjecture,
~ less_or_equal(additive_identity,u),
c_0_22 ).
cnf(c_0_32,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
cnf(c_0_33,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
c_0_23 ).
cnf(c_0_34,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
c_0_24 ).
cnf(c_0_35,negated_conjecture,
( ~ equalish(X1,a)
| equalish(add(X1,a),u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_36,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_28 ).
cnf(c_0_37,hypothesis,
less_or_equal(u,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_38,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
c_0_32 ).
cnf(c_0_39,negated_conjecture,
equalish(u,add(a,a)),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_40,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( ~ equalish(X1,a)
| equalish(u,add(X1,a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_42,hypothesis,
( ~ less_or_equal(X1,u)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( ~ less_or_equal(u,X1)
| less_or_equal(add(a,a),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,hypothesis,
less_or_equal(u,u),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_45,negated_conjecture,
( ~ equalish(additive_identity,a)
| equalish(u,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_27])]) ).
cnf(c_0_46,negated_conjecture,
less_or_equal(add(a,a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_48,negated_conjecture,
( ~ equalish(additive_identity,a)
| ~ less_or_equal(u,X1)
| less_or_equal(a,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( ~ less_or_equal(X1,add(a,a))
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_46]) ).
cnf(c_0_50,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
c_0_47 ).
cnf(c_0_51,hypothesis,
( ~ equalish(additive_identity,a)
| less_or_equal(a,u) ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_52,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_53,plain,
( ~ defined(X1)
| ~ less_or_equal(add(additive_identity,X1),X2)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( ~ less_or_equal(X1,a)
| less_or_equal(add(X1,a),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_27])]) ).
cnf(c_0_55,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_3 ).
cnf(c_0_56,hypothesis,
( ~ equalish(additive_identity,a)
| ~ less_or_equal(X1,a)
| less_or_equal(X1,u) ),
inference(spm,[status(thm)],[c_0_36,c_0_51]) ).
cnf(c_0_57,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
c_0_52 ).
cnf(c_0_58,negated_conjecture,
less_or_equal(a,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_27]),c_0_55])]) ).
cnf(c_0_59,negated_conjecture,
~ equalish(additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_56]),c_0_55])]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_55])]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.88 % Computer : n006.cluster.edu
% 0.19/5.88 % Model : x86_64 x86_64
% 0.19/5.88 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.88 % Memory : 8046.5625MB
% 0.19/5.88 % OS : Linux 6.8.0-71-generic
% 0.19/5.88 % CPULimit : 300
% 0.19/5.88 % WCLimit : 300
% 0.19/5.88 % DateTime : Mon Sep 21 15:43:18 UTC 2026
% 0.19/5.89 % CPUTime :
% 0.19/5.89 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/5.95 Running first-order theorem proving
% 0.23/5.96 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
% 0.23/5.99 % Version: 3.5.1
% 0.23/5.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.99 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.99 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.99 % Starting sh5l with 300s (1) cores
% 0.23/5.99 % new_bool_3 with pid 3185023 completed with status 0
% 0.23/5.99 % Result found by new_bool_3
% 0.23/5.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.99 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.99 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.99 % Search class: FGUNF-FFMS22-SFFFFFNN
% 0.23/5.99 % partial match(1): FGUNF-FFMS21-SFFFFFNN
% 0.23/5.99 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.99 % Starting SubtermCWHack with 28s (1) cores
% 0.23/5.99 % SubtermCWHack with pid 3185029 completed with status 0
% 0.23/5.99 % Result found by SubtermCWHack
% 0.23/5.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.99 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.99 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.99 % Search class: FGUNF-FFMS22-SFFFFFNN
% 0.23/5.99 % partial match(1): FGUNF-FFMS21-SFFFFFNN
% 0.23/5.99 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.99 % Starting SubtermCWHack with 28s (1) cores
% 0.23/5.99 % Preprocessing time : 0.001 s
% 0.23/5.99
% 0.23/5.99 % Proof found!
% 0.23/5.99 % SZS status Unsatisfiable
% 0.23/5.99 % SZS output start CNFRefutation
% See solution above
% 0.23/5.99 % Parsed axioms : 32
% 0.23/5.99 % Removed by relevancy pruning/SinE : 7
% 0.23/5.99 % Initial clauses : 25
% 0.23/5.99 % Removed in clause preprocessing : 0
% 0.23/5.99 % Initial clauses in saturation : 25
% 0.23/5.99 % Processed clauses : 102
% 0.23/5.99 % ...of these trivial : 0
% 0.23/5.99 % ...subsumed : 22
% 0.23/5.99 % ...remaining for further processing : 80
% 0.23/5.99 % Other redundant clauses eliminated : 0
% 0.23/5.99 % Clauses deleted for lack of memory : 0
% 0.23/5.99 % Backward-subsumed : 10
% 0.23/5.99 % Backward-rewritten : 1
% 0.23/5.99 % Generated clauses : 235
% 0.23/5.99 % ...of the previous two non-redundant : 173
% 0.23/5.99 % ...aggressively subsumed : 0
% 0.23/5.99 % Contextual simplify-reflections : 0
% 0.23/5.99 % Paramodulations : 235
% 0.23/5.99 % Factorizations : 0
% 0.23/5.99 % NegExts : 0
% 0.23/5.99 % Equation resolutions : 0
% 0.23/5.99 % Disequality decompositions : 0
% 0.23/5.99 % Total rewrite steps : 78
% 0.23/5.99 % ...of those cached : 63
% 0.23/5.99 % Propositional unsat checks : 0
% 0.23/5.99 % Propositional check models : 0
% 0.23/5.99 % Propositional check unsatisfiable : 0
% 0.23/5.99 % Propositional clauses : 0
% 0.23/5.99 % Propositional clauses after purity: 0
% 0.23/5.99 % Propositional unsat core size : 0
% 0.23/5.99 % Propositional preprocessing time : 0.000
% 0.23/5.99 % Propositional encoding time : 0.000
% 0.23/5.99 % Propositional solver time : 0.000
% 0.23/5.99 % Success case prop preproc time : 0.000
% 0.23/5.99 % Success case prop encoding time : 0.000
% 0.23/5.99 % Success case prop solver time : 0.000
% 0.23/5.99 % Current number of processed clauses : 69
% 0.23/5.99 % Positive orientable unit clauses : 17
% 0.23/5.99 % Positive unorientable unit clauses: 0
% 0.23/5.99 % Negative unit clauses : 2
% 0.23/5.99 % Non-unit-clauses : 50
% 0.23/5.99 % Current number of unprocessed clauses: 91
% 0.23/5.99 % ...number of literals in the above : 315
% 0.23/5.99 % Current number of archived formulas : 0
% 0.23/5.99 % Current number of archived clauses : 11
% 0.23/5.99 % Clause-clause subsumption calls (NU) : 232
% 0.23/5.99 % Rec. Clause-clause subsumption calls : 219
% 0.23/5.99 % Non-unit clause-clause subsumptions : 21
% 0.23/5.99 % Unit Clause-clause subsumption calls : 19
% 0.23/5.99 % Rewrite failures with RHS unbound : 0
% 0.23/5.99 % BW rewrite match attempts : 2
% 0.23/5.99 % BW rewrite match successes : 2
% 0.23/5.99 % Condensation attempts : 0
% 0.23/5.99 % Condensation successes : 0
% 0.23/5.99 % Termbank termtop insertions : 3477
% 0.23/5.99 % Search garbage collected termcells : 93
% 0.23/5.99
% 0.23/5.99 % -------------------------------------------------
% 0.23/5.99 % User time : 0.009 s
% 0.23/5.99 % System time : 0.002 s
% 0.23/5.99 % Total time : 0.011 s
% 0.23/5.99 % Maximum resident set size: 3660 pages
% 0.23/5.99
% 0.23/5.99 % -------------------------------------------------
% 0.23/5.99 % User time : 0.012 s
% 0.23/5.99 % System time : 0.008 s
% 0.23/5.99 % Total time : 0.020 s
% 0.23/5.99 % Maximum resident set size: 4864 pages
% 0.23/5.99 % E exiting
%------------------------------------------------------------------------------