%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD008-4 : 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 : n003.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 12:22:38 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.47s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 61 ( 24 unt; 0 nHn; 61 RR)
% Number of literals : 120 ( 0 equ; 62 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(sum_5,negated_conjecture,
sum(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_5) ).
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_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(sum_6,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
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(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(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
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,
( ~ 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_15,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_16,negated_conjecture,
sum(a,b,c),
sum_5 ).
cnf(c_0_17,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_18,negated_conjecture,
sum(b,a,c),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,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_20,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_21,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
sum_6 ).
cnf(c_0_22,negated_conjecture,
( ~ sum(X1,X3,b)
| ~ sum(X3,a,X2)
| sum(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_19 ).
cnf(c_0_24,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_20 ).
cnf(c_0_25,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_26,negated_conjecture,
sum(additive_inverse(b),additive_inverse(a),d),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( ~ sum(X1,b,b)
| sum(X1,c,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ defined(X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_30,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_25 ).
cnf(c_0_31,negated_conjecture,
( ~ sum(X1,X3,additive_inverse(b))
| ~ sum(X3,additive_inverse(a),X2)
| sum(X1,X2,d) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( ~ sum(X1,b,b)
| sum(c,X1,c) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_33,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_34,negated_conjecture,
( ~ sum(additive_inverse(b),additive_identity,X1)
| sum(d,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29])]) ).
cnf(c_0_35,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ sum(X1,additive_inverse(b),additive_inverse(b))
| sum(X1,d,d) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_37,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_38,negated_conjecture,
sum(c,additive_identity,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_33])]) ).
cnf(c_0_39,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_inverse(X3))
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_40,negated_conjecture,
( ~ defined(additive_inverse(b))
| sum(d,a,additive_inverse(b)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( ~ defined(additive_inverse(b))
| sum(additive_identity,d,d) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_42,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_37 ).
cnf(c_0_43,negated_conjecture,
sum(additive_identity,c,c),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( ~ sum(a,b,X1)
| ~ defined(additive_inverse(b))
| sum(d,X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_33])]) ).
cnf(c_0_45,negated_conjecture,
sum(additive_identity,d,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).
cnf(c_0_46,negated_conjecture,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,c,X2)
| sum(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ sum(a,b,X1)
| sum(d,X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,d,X2)
| sum(X1,d,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_49,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_50,negated_conjecture,
( ~ sum(X1,d,additive_identity)
| sum(X1,additive_identity,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_16])]) ).
cnf(c_0_51,negated_conjecture,
( ~ sum(additive_inverse(d),additive_identity,X1)
| sum(X1,d,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_24]),c_0_49])]) ).
cnf(c_0_52,negated_conjecture,
sum(additive_inverse(d),additive_identity,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_49])]) ).
cnf(c_0_53,negated_conjecture,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,d,X2)
| sum(X1,X2,d) ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
sum(c,d,additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ~ sum(X1,c,additive_identity)
| sum(X1,additive_identity,d) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_57,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
inference(fof_simplification,[status(thm)],[not_sum_7]) ).
cnf(c_0_58,negated_conjecture,
sum(additive_inverse(c),additive_identity,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_24]),c_0_56])]) ).
cnf(c_0_59,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
c_0_57 ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 15:38:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.30/0.47 % Version: 3.5.1
% 0.30/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.47 % Starting sh5l with 300s (1) cores
% 0.30/0.47 % new_bool_1 with pid 462856 completed with status 0
% 0.30/0.47 % Result found by new_bool_1
% 0.30/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.30/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.30/0.47 % Search class: FHUNF-FFSM11-SFFFFFNN
% 0.30/0.47 % partial match(1): FHUNF-FFSF11-SFFFFFNN
% 0.30/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.30/0.47 % SubtermCWHack with pid 462863 completed with status 0
% 0.30/0.47 % Result found by SubtermCWHack
% 0.30/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.30/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.30/0.47 % Search class: FHUNF-FFSM11-SFFFFFNN
% 0.30/0.47 % partial match(1): FHUNF-FFSF11-SFFFFFNN
% 0.30/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.30/0.47 % Preprocessing time : 0.001 s
% 0.30/0.47
% 0.30/0.47 % Proof found!
% 0.30/0.47 % SZS status Unsatisfiable
% 0.30/0.47 % SZS output start CNFRefutation
% See solution above
% 0.30/0.47 % Parsed axioms : 33
% 0.30/0.47 % Removed by relevancy pruning/SinE : 19
% 0.30/0.47 % Initial clauses : 14
% 0.30/0.47 % Removed in clause preprocessing : 0
% 0.30/0.47 % Initial clauses in saturation : 14
% 0.30/0.47 % Processed clauses : 452
% 0.30/0.47 % ...of these trivial : 5
% 0.30/0.47 % ...subsumed : 152
% 0.30/0.47 % ...remaining for further processing : 295
% 0.30/0.47 % Other redundant clauses eliminated : 0
% 0.30/0.47 % Clauses deleted for lack of memory : 0
% 0.30/0.47 % Backward-subsumed : 14
% 0.30/0.47 % Backward-rewritten : 1
% 0.30/0.47 % Generated clauses : 1531
% 0.30/0.47 % ...of the previous two non-redundant : 1306
% 0.30/0.47 % ...aggressively subsumed : 0
% 0.30/0.47 % Contextual simplify-reflections : 1
% 0.30/0.47 % Paramodulations : 1531
% 0.30/0.47 % Factorizations : 0
% 0.30/0.47 % NegExts : 0
% 0.30/0.47 % Equation resolutions : 0
% 0.30/0.47 % Disequality decompositions : 0
% 0.30/0.47 % Total rewrite steps : 624
% 0.30/0.47 % ...of those cached : 602
% 0.30/0.47 % Propositional unsat checks : 0
% 0.30/0.47 % Propositional check models : 0
% 0.30/0.47 % Propositional check unsatisfiable : 0
% 0.30/0.47 % Propositional clauses : 0
% 0.30/0.47 % Propositional clauses after purity: 0
% 0.30/0.47 % Propositional unsat core size : 0
% 0.30/0.47 % Propositional preprocessing time : 0.000
% 0.30/0.47 % Propositional encoding time : 0.000
% 0.30/0.47 % Propositional solver time : 0.000
% 0.30/0.47 % Success case prop preproc time : 0.000
% 0.30/0.47 % Success case prop encoding time : 0.000
% 0.30/0.47 % Success case prop solver time : 0.000
% 0.30/0.47 % Current number of processed clauses : 280
% 0.30/0.47 % Positive orientable unit clauses : 25
% 0.30/0.47 % Positive unorientable unit clauses: 0
% 0.30/0.47 % Negative unit clauses : 1
% 0.30/0.47 % Non-unit-clauses : 254
% 0.30/0.47 % Current number of unprocessed clauses: 863
% 0.30/0.47 % ...number of literals in the above : 2925
% 0.30/0.47 % Current number of archived formulas : 0
% 0.30/0.47 % Current number of archived clauses : 15
% 0.30/0.47 % Clause-clause subsumption calls (NU) : 3707
% 0.30/0.47 % Rec. Clause-clause subsumption calls : 3641
% 0.30/0.47 % Non-unit clause-clause subsumptions : 161
% 0.30/0.47 % Unit Clause-clause subsumption calls : 12
% 0.30/0.47 % Rewrite failures with RHS unbound : 0
% 0.30/0.47 % BW rewrite match attempts : 18
% 0.30/0.47 % BW rewrite match successes : 5
% 0.30/0.47 % Condensation attempts : 0
% 0.30/0.47 % Condensation successes : 0
% 0.30/0.47 % Termbank termtop insertions : 18601
% 0.30/0.47 % Search garbage collected termcells : 151
% 0.30/0.47
% 0.30/0.47 % -------------------------------------------------
% 0.30/0.47 % User time : 0.030 s
% 0.30/0.47 % System time : 0.007 s
% 0.30/0.47 % Total time : 0.037 s
% 0.30/0.47 % Maximum resident set size: 3660 pages
% 0.30/0.47
% 0.30/0.47 % -------------------------------------------------
% 0.30/0.47 % User time : 0.032 s
% 0.30/0.47 % System time : 0.012 s
% 0.30/0.47 % Total time : 0.044 s
% 0.30/0.47 % Maximum resident set size: 4608 pages
% 0.30/0.47 % E exiting
%------------------------------------------------------------------------------