%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD070-2 : 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 : n010.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 12:22:57 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 70 ( 25 unt; 4 nHn; 70 RR)
% Number of literals : 147 ( 0 equ; 77 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_equality,axiom,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(add_equals_c_4,negated_conjecture,
equalish(add(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_c_4) ).
cnf(commutativity_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
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/FLD001-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_less_or_equal_7,negated_conjecture,
~ less_or_equal(additive_identity,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_7) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.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/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(less_or_equal_5,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_5) ).
cnf(less_or_equal_6,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_6) ).
cnf(c_0_18,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_equality]) ).
cnf(c_0_19,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
c_0_18 ).
cnf(c_0_20,negated_conjecture,
equalish(add(a,b),c),
add_equals_c_4 ).
cnf(c_0_21,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_22,negated_conjecture,
( ~ equalish(X1,add(a,b))
| equalish(X1,c) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
c_0_21 ).
cnf(c_0_24,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_25,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_26,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_27,negated_conjecture,
equalish(add(b,a),c),
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])]) ).
cnf(c_0_28,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_29,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_26 ).
cnf(c_0_30,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_31,negated_conjecture,
~ less_or_equal(additive_identity,c),
inference(fof_simplification,[status(thm)],[not_less_or_equal_7]) ).
cnf(c_0_32,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[symmetry_of_equality]) ).
cnf(c_0_33,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_34,negated_conjecture,
( ~ equalish(X1,add(b,a))
| equalish(X1,c) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_35,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
c_0_28 ).
cnf(c_0_36,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_37,hypothesis,
( ~ defined(X1)
| less_or_equal(X1,c)
| less_or_equal(c,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_39,negated_conjecture,
~ less_or_equal(additive_identity,c),
c_0_31 ).
cnf(c_0_40,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_41,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
c_0_32 ).
cnf(c_0_42,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
c_0_33 ).
cnf(c_0_43,negated_conjecture,
( ~ equalish(X1,b)
| equalish(add(X1,a),c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24])]) ).
cnf(c_0_44,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_36 ).
cnf(c_0_45,hypothesis,
less_or_equal(c,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
c_0_40 ).
cnf(c_0_47,negated_conjecture,
equalish(c,add(a,b)),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_48,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( ~ equalish(X1,b)
| equalish(c,add(X1,a)) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_50,hypothesis,
( ~ less_or_equal(X1,c)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( ~ less_or_equal(c,X1)
| less_or_equal(add(a,b),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,hypothesis,
less_or_equal(c,c),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_53,negated_conjecture,
( ~ equalish(additive_identity,b)
| equalish(c,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24])]) ).
cnf(c_0_54,negated_conjecture,
less_or_equal(add(a,b),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_55,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_56,negated_conjecture,
( ~ equalish(additive_identity,b)
| ~ less_or_equal(c,X1)
| less_or_equal(a,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( ~ less_or_equal(X1,add(a,b))
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_54]) ).
cnf(c_0_58,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
c_0_55 ).
cnf(c_0_59,hypothesis,
( ~ equalish(additive_identity,b)
| less_or_equal(a,c) ),
inference(spm,[status(thm)],[c_0_56,c_0_52]) ).
cnf(c_0_60,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_61,plain,
( ~ defined(X1)
| ~ less_or_equal(add(additive_identity,X1),X2)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_42]) ).
cnf(c_0_62,negated_conjecture,
( ~ less_or_equal(X1,a)
| less_or_equal(add(X1,b),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_25])]) ).
cnf(c_0_63,negated_conjecture,
less_or_equal(additive_identity,a),
less_or_equal_5 ).
cnf(c_0_64,hypothesis,
( ~ equalish(additive_identity,b)
| ~ less_or_equal(X1,a)
| less_or_equal(X1,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_59]) ).
cnf(c_0_65,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
c_0_60 ).
cnf(c_0_66,negated_conjecture,
less_or_equal(b,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_25]),c_0_63])]) ).
cnf(c_0_67,negated_conjecture,
less_or_equal(additive_identity,b),
less_or_equal_6 ).
cnf(c_0_68,negated_conjecture,
~ equalish(additive_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_64]),c_0_63])]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 15:44:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % new_bool_3 with pid 1210126 completed with status 0
% 0.15/0.44 % Result found by new_bool_3
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUNF-FFMM22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 1210131 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUNF-FFMM22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % Preprocessing time : 0.001 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 34
% 0.15/0.44 % Removed by relevancy pruning/SinE : 7
% 0.15/0.44 % Initial clauses : 27
% 0.15/0.44 % Removed in clause preprocessing : 0
% 0.15/0.44 % Initial clauses in saturation : 27
% 0.15/0.44 % Processed clauses : 191
% 0.15/0.44 % ...of these trivial : 0
% 0.15/0.44 % ...subsumed : 48
% 0.15/0.44 % ...remaining for further processing : 143
% 0.15/0.44 % Other redundant clauses eliminated : 0
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 32
% 0.15/0.44 % Backward-rewritten : 5
% 0.15/0.44 % Generated clauses : 504
% 0.15/0.44 % ...of the previous two non-redundant : 358
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 504
% 0.15/0.44 % Factorizations : 0
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 0
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 227
% 0.15/0.44 % ...of those cached : 201
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 106
% 0.15/0.44 % Positive orientable unit clauses : 30
% 0.15/0.44 % Positive unorientable unit clauses: 0
% 0.15/0.44 % Negative unit clauses : 3
% 0.15/0.44 % Non-unit-clauses : 73
% 0.15/0.44 % Current number of unprocessed clauses: 153
% 0.15/0.44 % ...number of literals in the above : 518
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 37
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 718
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 654
% 0.15/0.44 % Non-unit clause-clause subsumptions : 47
% 0.15/0.44 % Unit Clause-clause subsumption calls : 62
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 4
% 0.15/0.44 % BW rewrite match successes : 4
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 6447
% 0.15/0.44 % Search garbage collected termcells : 93
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.013 s
% 0.15/0.44 % System time : 0.003 s
% 0.15/0.44 % Total time : 0.016 s
% 0.15/0.44 % Maximum resident set size: 3660 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.018 s
% 0.15/0.44 % System time : 0.005 s
% 0.15/0.44 % Total time : 0.023 s
% 0.15/0.44 % Maximum resident set size: 4608 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------