%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD008-3 : 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 : n002.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 12:23:06 PM UTC 2026
% Result : Unsatisfiable 221.47s 32.57s
% Output : CNFRefutation 221.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 49 ( 9 unt; 0 nHn; 49 RR)
% Number of literals : 130 ( 0 equ; 91 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
cnf(totality_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
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(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_0_11,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_12,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_13,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_11 ).
cnf(c_0_14,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_12 ).
cnf(c_0_15,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_16,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_17,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_15 ).
cnf(c_0_19,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_16 ).
cnf(c_0_20,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
inference(fof_simplification,[status(thm)],[not_sum_3]) ).
cnf(c_0_21,plain,
( ~ sum(X1,X3,X2)
| ~ defined(X1)
| ~ defined(X3)
| sum(additive_inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_25,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
c_0_20 ).
cnf(c_0_26,plain,
( ~ sum(X2,X3,X1)
| ~ defined(X2)
| ~ defined(X3)
| sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_27,plain,
( ~ sum(X1,X4,X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_28,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_23 ).
cnf(c_0_29,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_24 ).
cnf(c_0_30,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_31,negated_conjecture,
( ~ sum(add(a,b),add(additive_inverse(a),additive_inverse(b)),additive_identity)
| ~ defined(add(a,b))
| ~ defined(add(additive_inverse(a),additive_inverse(b))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( ~ sum(X1,X2,X3)
| ~ defined(X2)
| ~ defined(X3)
| sum(X1,add(X2,additive_inverse(X3)),additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_34,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_35,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_36,negated_conjecture,
( ~ sum(add(a,b),additive_inverse(a),b)
| ~ defined(additive_inverse(a))
| ~ defined(add(a,b))
| ~ defined(add(additive_inverse(a),additive_inverse(b))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_34 ).
cnf(c_0_38,plain,
( ~ sum(X4,X2,X1)
| ~ sum(X4,additive_identity,X3)
| ~ defined(X2)
| sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( ~ sum(add(a,b),additive_inverse(a),b)
| ~ defined(additive_inverse(b))
| ~ defined(additive_inverse(a))
| ~ defined(add(a,b)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( ~ sum(X3,X2,X1)
| ~ defined(X3)
| ~ defined(X2)
| sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_43,negated_conjecture,
( ~ sum(b,a,add(a,b))
| ~ defined(additive_inverse(b))
| ~ defined(additive_inverse(a))
| ~ defined(add(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_33])]) ).
cnf(c_0_44,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_45,negated_conjecture,
( ~ defined(additive_inverse(b))
| ~ defined(additive_inverse(a))
| ~ defined(add(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_33]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( ~ defined(additive_inverse(b))
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_33]),c_0_42])]) ).
cnf(c_0_47,negated_conjecture,
~ defined(additive_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_29]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_29]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD008-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:39:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 221.47/32.57 % Version: 3.5.1
% 221.47/32.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 221.47/32.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.47/32.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 221.47/32.57 % Starting new_bool_3 with 300s (1) cores
% 221.47/32.57 % Starting new_bool_1 with 300s (1) cores
% 221.47/32.57 % Starting sh5l with 300s (1) cores
% 221.47/32.57 % new_bool_1 with pid 3625865 completed with status 0
% 221.47/32.57 % Result found by new_bool_1
% 221.47/32.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 221.47/32.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.47/32.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 221.47/32.57 % Starting new_bool_3 with 300s (1) cores
% 221.47/32.57 % Starting new_bool_1 with 300s (1) cores
% 221.47/32.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.47/32.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.47/32.57 % Search class: FHUNF-FFSS21-SFFFFFNN
% 221.47/32.57 % partial match(1): FHUNF-FFSF21-SFFFFFNN
% 221.47/32.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.47/32.57 % Starting SubtermCWHack with 31s (1) cores
% 221.47/32.57 % SubtermCWHack with pid 3625873 completed with status 8
% 221.47/32.57 % Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 221.47/32.57 % SAT001_MinMin_p005000_rr_RG with pid 3626832 completed with status 0
% 221.47/32.57 % Result found by SAT001_MinMin_p005000_rr_RG
% 221.47/32.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 221.47/32.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.47/32.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 221.47/32.57 % Starting new_bool_3 with 300s (1) cores
% 221.47/32.57 % Starting new_bool_1 with 300s (1) cores
% 221.47/32.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.47/32.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.47/32.57 % Search class: FHUNF-FFSS21-SFFFFFNN
% 221.47/32.57 % partial match(1): FHUNF-FFSF21-SFFFFFNN
% 221.47/32.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.47/32.57 % Starting SubtermCWHack with 31s (1) cores
% 221.47/32.57 % SubtermCWHack with pid 3625873 completed with status 8
% 221.47/32.57 % Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 221.47/32.57 % Preprocessing time : 0.001 s
% 221.47/32.57 % Presaturation interreduction done
% 221.47/32.57
% 221.47/32.57 % Proof found!
% 221.47/32.57 % SZS status Unsatisfiable
% 221.47/32.57 % SZS output start CNFRefutation
% See solution above
% 221.47/32.57 % Parsed axioms : 29
% 221.47/32.57 % Removed by relevancy pruning/SinE : 17
% 221.47/32.57 % Initial clauses : 12
% 221.47/32.57 % Removed in clause preprocessing : 0
% 221.47/32.57 % Initial clauses in saturation : 12
% 221.47/32.57 % Processed clauses : 3083
% 221.47/32.57 % ...of these trivial : 19
% 221.47/32.57 % ...subsumed : 2445
% 221.47/32.57 % ...remaining for further processing : 619
% 221.47/32.57 % Other redundant clauses eliminated : 0
% 221.47/32.57 % Clauses deleted for lack of memory : 0
% 221.47/32.57 % Backward-subsumed : 31
% 221.47/32.57 % Backward-rewritten : 0
% 221.47/32.57 % Generated clauses : 27267
% 221.47/32.57 % ...of the previous two non-redundant : 24704
% 221.47/32.57 % ...aggressively subsumed : 0
% 221.47/32.57 % Contextual simplify-reflections : 46
% 221.47/32.57 % Paramodulations : 27267
% 221.47/32.57 % Factorizations : 0
% 221.47/32.57 % NegExts : 0
% 221.47/32.57 % Equation resolutions : 0
% 221.47/32.57 % Disequality decompositions : 0
% 221.47/32.57 % Total rewrite steps : 12787
% 221.47/32.57 % ...of those cached : 12771
% 221.47/32.57 % Propositional unsat checks : 0
% 221.47/32.57 % Propositional check models : 0
% 221.47/32.57 % Propositional check unsatisfiable : 0
% 221.47/32.57 % Propositional clauses : 0
% 221.47/32.57 % Propositional clauses after purity: 0
% 221.47/32.57 % Propositional unsat core size : 0
% 221.47/32.57 % Propositional preprocessing time : 0.000
% 221.47/32.57 % Propositional encoding time : 0.000
% 221.47/32.57 % Propositional solver time : 0.000
% 221.47/32.57 % Success case prop preproc time : 0.000
% 221.47/32.57 % Success case prop encoding time : 0.000
% 221.47/32.57 % Success case prop solver time : 0.000
% 221.47/32.57 % Current number of processed clauses : 576
% 221.47/32.57 % Positive orientable unit clauses : 16
% 221.47/32.57 % Positive unorientable unit clauses: 0
% 221.47/32.57 % Negative unit clauses : 2
% 221.47/32.57 % Non-unit-clauses : 558
% 221.47/32.57 % Current number of unprocessed clauses: 21591
% 221.47/32.57 % ...number of literals in the above : 99103
% 221.47/32.57 % Current number of archived formulas : 0
% 221.47/32.57 % Current number of archived clauses : 43
% 221.47/32.57 % Clause-clause subsumption calls (NU) : 84223
% 221.47/32.57 % Rec. Clause-clause subsumption calls : 62803
% 221.47/32.57 % Non-unit clause-clause subsumptions : 2509
% 221.47/32.57 % Unit Clause-clause subsumption calls : 141
% 221.47/32.57 % Rewrite failures with RHS unbound : 0
% 221.47/32.57 % BW rewrite match attempts : 27
% 221.47/32.57 % BW rewrite match successes : 8
% 221.47/32.57 % Condensation attempts : 0
% 221.47/32.57 % Condensation successes : 0
% 221.47/32.57 % Termbank termtop insertions : 454962
% 221.47/32.57 % Search garbage collected termcells : 146
% 221.47/32.57
% 221.47/32.57 % -------------------------------------------------
% 221.47/32.57 % User time : 30.490 s
% 221.47/32.57 % System time : 1.115 s
% 221.47/32.57 % Total time : 31.604 s
% 221.47/32.57 % Maximum resident set size: 3660 pages
% 221.47/32.57
% 221.47/32.57 % -------------------------------------------------
% 221.47/32.57 % User time : 30.491 s
% 221.47/32.57 % System time : 1.121 s
% 221.47/32.57 % Total time : 31.612 s
% 221.47/32.57 % Maximum resident set size: 4608 pages
% 221.47/32.57 % E exiting
%------------------------------------------------------------------------------