%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD014-3 : 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 : n017.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 12:22:40 PM UTC 2026
% Result : Unsatisfiable 1.09s 0.69s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 62 ( 26 unt; 4 nHn; 62 RR)
% Number of literals : 125 ( 0 equ; 62 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
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/FLD002-0.ax',totality_of_order_relation) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(sum_3,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_13,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_14,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_15,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_16,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_17,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_18,negated_conjecture,
sum(additive_identity,a,b),
sum_3 ).
cnf(c_0_19,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_14 ).
cnf(c_0_20,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_21,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_15 ).
cnf(c_0_22,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_16 ).
cnf(c_0_23,negated_conjecture,
sum(a,additive_identity,b),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
( ~ defined(X1)
| less_or_equal(X1,a)
| less_or_equal(a,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,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_27,negated_conjecture,
( ~ sum(X2,additive_identity,X1)
| ~ less_or_equal(X2,a)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_29,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_30,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_26 ).
cnf(c_0_31,hypothesis,
less_or_equal(a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,hypothesis,
( ~ sum(X2,additive_identity,X1)
| ~ less_or_equal(X2,a)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_33,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_34,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_35,hypothesis,
( ~ less_or_equal(b,a)
| sum(additive_identity,b,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
less_or_equal(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_29])]) ).
cnf(c_0_37,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_33 ).
cnf(c_0_38,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_19,c_0_34]) ).
cnf(c_0_39,hypothesis,
sum(additive_identity,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_41,plain,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,hypothesis,
sum(b,additive_identity,a),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_43,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_44,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_40 ).
cnf(c_0_45,hypothesis,
( ~ sum(X1,b,additive_identity)
| sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_43 ).
cnf(c_0_47,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_48,negated_conjecture,
( ~ sum(X1,a,additive_identity)
| sum(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_49,plain,
( ~ defined(X1)
| sum(additive_identity,additive_inverse(X1),additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_44]) ).
cnf(c_0_50,hypothesis,
sum(additive_inverse(b),a,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_51,negated_conjecture,
( ~ sum(X1,a,additive_identity)
| sum(b,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_48]) ).
cnf(c_0_52,plain,
( ~ sum(X1,X4,additive_identity)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_49]) ).
cnf(c_0_53,hypothesis,
sum(a,additive_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_17,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
sum(b,additive_inverse(a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_20])]) ).
cnf(c_0_55,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_56,hypothesis,
( ~ sum(X1,a,additive_identity)
| sum(X1,additive_identity,additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_47])]) ).
cnf(c_0_57,negated_conjecture,
sum(additive_inverse(a),b,additive_identity),
inference(spm,[status(thm)],[c_0_17,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
c_0_55 ).
cnf(c_0_59,hypothesis,
( ~ sum(X1,a,additive_identity)
| sum(additive_identity,X1,additive_inverse(b)) ),
inference(spm,[status(thm)],[c_0_17,c_0_56]) ).
cnf(c_0_60,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 15:32:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 1.09/0.69 % Version: 3.5.1
% 1.09/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.09/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.09/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.09/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.09/0.69 % Starting sh5l with 300s (1) cores
% 1.09/0.69 % sh5l with pid 2659807 completed with status 0
% 1.09/0.69 % Result found by sh5l
% 1.09/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.09/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.09/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.09/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.09/0.69 % Starting sh5l with 300s (1) cores
% 1.09/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.09/0.69 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.09/0.69 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.09/0.69 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 1.09/0.69 % Starting SubtermCWHack with 28s (1) cores
% 1.09/0.69 % SubtermCWHack with pid 2659815 completed with status 0
% 1.09/0.69 % Result found by SubtermCWHack
% 1.09/0.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.09/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.09/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.09/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.09/0.69 % Starting sh5l with 300s (1) cores
% 1.09/0.69 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.09/0.69 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.09/0.69 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.09/0.69 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 1.09/0.69 % Starting SubtermCWHack with 28s (1) cores
% 1.09/0.69 % Preprocessing time : 0.002 s
% 1.09/0.69
% 1.09/0.69 % Proof found!
% 1.09/0.69 % SZS status Unsatisfiable
% 1.09/0.69 % SZS output start CNFRefutation
% See solution above
% 1.09/0.69 % Parsed axioms : 30
% 1.09/0.69 % Removed by relevancy pruning/SinE : 2
% 1.09/0.69 % Initial clauses : 28
% 1.09/0.69 % Removed in clause preprocessing : 0
% 1.09/0.69 % Initial clauses in saturation : 28
% 1.09/0.69 % Processed clauses : 1354
% 1.09/0.69 % ...of these trivial : 0
% 1.09/0.69 % ...subsumed : 693
% 1.09/0.69 % ...remaining for further processing : 661
% 1.09/0.69 % Other redundant clauses eliminated : 0
% 1.09/0.69 % Clauses deleted for lack of memory : 0
% 1.09/0.69 % Backward-subsumed : 16
% 1.09/0.69 % Backward-rewritten : 5
% 1.09/0.69 % Generated clauses : 5717
% 1.09/0.69 % ...of the previous two non-redundant : 4797
% 1.09/0.69 % ...aggressively subsumed : 0
% 1.09/0.69 % Contextual simplify-reflections : 0
% 1.09/0.69 % Paramodulations : 5717
% 1.09/0.69 % Factorizations : 0
% 1.09/0.69 % NegExts : 0
% 1.09/0.69 % Equation resolutions : 0
% 1.09/0.69 % Disequality decompositions : 0
% 1.09/0.69 % Total rewrite steps : 1869
% 1.09/0.69 % ...of those cached : 1828
% 1.09/0.69 % Propositional unsat checks : 0
% 1.09/0.69 % Propositional check models : 0
% 1.09/0.69 % Propositional check unsatisfiable : 0
% 1.09/0.69 % Propositional clauses : 0
% 1.09/0.69 % Propositional clauses after purity: 0
% 1.09/0.69 % Propositional unsat core size : 0
% 1.09/0.69 % Propositional preprocessing time : 0.000
% 1.09/0.69 % Propositional encoding time : 0.000
% 1.09/0.69 % Propositional solver time : 0.000
% 1.09/0.69 % Success case prop preproc time : 0.000
% 1.09/0.69 % Success case prop encoding time : 0.000
% 1.09/0.69 % Success case prop solver time : 0.000
% 1.09/0.69 % Current number of processed clauses : 640
% 1.09/0.69 % Positive orientable unit clauses : 44
% 1.09/0.69 % Positive unorientable unit clauses: 0
% 1.09/0.69 % Negative unit clauses : 2
% 1.09/0.69 % Non-unit-clauses : 594
% 1.09/0.69 % Current number of unprocessed clauses: 3393
% 1.09/0.69 % ...number of literals in the above : 11814
% 1.09/0.69 % Current number of archived formulas : 0
% 1.09/0.69 % Current number of archived clauses : 21
% 1.09/0.69 % Clause-clause subsumption calls (NU) : 30607
% 1.09/0.69 % Rec. Clause-clause subsumption calls : 24790
% 1.09/0.69 % Non-unit clause-clause subsumptions : 709
% 1.09/0.69 % Unit Clause-clause subsumption calls : 540
% 1.09/0.69 % Rewrite failures with RHS unbound : 0
% 1.09/0.69 % BW rewrite match attempts : 12
% 1.09/0.69 % BW rewrite match successes : 2
% 1.09/0.69 % Condensation attempts : 0
% 1.09/0.69 % Condensation successes : 0
% 1.09/0.69 % Termbank termtop insertions : 68725
% 1.09/0.69 % Search garbage collected termcells : 121
% 1.09/0.69
% 1.09/0.69 % -------------------------------------------------
% 1.09/0.69 % User time : 0.170 s
% 1.09/0.69 % System time : 0.010 s
% 1.09/0.69 % Total time : 0.181 s
% 1.09/0.69 % Maximum resident set size: 3660 pages
% 1.09/0.69
% 1.09/0.69 % -------------------------------------------------
% 1.09/0.69 % User time : 0.173 s
% 1.09/0.69 % System time : 0.018 s
% 1.09/0.69 % Total time : 0.190 s
% 1.09/0.69 % Maximum resident set size: 4864 pages
% 1.09/0.69 % E exiting
%------------------------------------------------------------------------------