%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD010-5 : 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 : n014.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 12:22:39 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 20 unt; 9 nHn; 60 RR)
% Number of literals : 138 ( 0 equ; 75 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 113 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_1,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_1) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(distributivity_1,axiom,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
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(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
cnf(c_0_13,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_14,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_15,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_13 ).
cnf(c_0_16,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_17,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_18,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_19,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_21,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_1]) ).
cnf(c_0_22,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_23,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_17 ).
cnf(c_0_24,plain,
( ~ product(X3,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_20 ).
cnf(c_0_26,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
c_0_21 ).
cnf(c_0_27,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_22 ).
cnf(c_0_28,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_identity,multiplicative_inverse(X1),multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_29,plain,
( ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16])]),c_0_26]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),multiplicative_identity,multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_32,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16])]),c_0_26]) ).
cnf(c_0_33,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_31 ).
cnf(c_0_34,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_35,plain,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(multiplicative_identity),X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,plain,
( ~ product(X1,multiplicative_identity,multiplicative_identity)
| product(X1,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_16])]),c_0_26]) ).
cnf(c_0_37,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_38,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_39,plain,
( ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_inverse(multiplicative_identity),X1)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_40,plain,
( ~ product(X1,multiplicative_identity,multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_42,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_37 ).
cnf(c_0_43,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_44,plain,
( ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1)
| product(multiplicative_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_32])]) ).
cnf(c_0_45,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_46,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_41 ).
cnf(c_0_47,plain,
( ~ sum(X4,X3,multiplicative_identity)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_48,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_49,plain,
( ~ defined(X3)
| ~ product(X4,multiplicative_identity,X2)
| ~ product(X1,X4,multiplicative_inverse(X3))
| sum(additive_identity,X3,additive_identity)
| product(X1,X2,multiplicative_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_50,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_16])]),c_0_26]) ).
cnf(c_0_51,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_45 ).
cnf(c_0_52,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_46,c_0_16]) ).
cnf(c_0_53,plain,
( ~ sum(X2,additive_identity,multiplicative_identity)
| ~ product(X2,multiplicative_identity,X1)
| sum(X1,additive_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(multiplicative_identity,X1,multiplicative_inverse(multiplicative_identity)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_16])]),c_0_26]) ).
cnf(c_0_55,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(fof_simplification,[status(thm)],[not_sum_2]) ).
cnf(c_0_57,plain,
sum(multiplicative_inverse(multiplicative_identity),additive_identity,multiplicative_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_55]),c_0_19])]) ).
cnf(c_0_58,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
c_0_56 ).
cnf(c_0_59,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 % Computer : n014.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Mon Sep 21 15:37:49 UTC 2026
% 0.16/0.46 % CPUTime :
% 0.16/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.52 Running first-order theorem proving
% 0.21/0.52 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
% 0.21/0.61 % Version: 3.5.1
% 0.21/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.61 % Starting sh5l with 300s (1) cores
% 0.21/0.61 % new_bool_3 with pid 222080 completed with status 0
% 0.21/0.61 % Result found by new_bool_3
% 0.21/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.61 % Search class: FGUNF-FFSF11-SFFFFFNN
% 0.21/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.61 % SubtermCWHack with pid 222083 completed with status 0
% 0.21/0.61 % Result found by SubtermCWHack
% 0.21/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.61 % Search class: FGUNF-FFSF11-SFFFFFNN
% 0.21/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.61 % Preprocessing time : 0.001 s
% 0.21/0.61
% 0.21/0.61 % Proof found!
% 0.21/0.61 % SZS status Unsatisfiable
% 0.21/0.61 % SZS output start CNFRefutation
% See solution above
% 0.21/0.61 % Parsed axioms : 28
% 0.21/0.61 % Removed by relevancy pruning/SinE : 11
% 0.21/0.61 % Initial clauses : 17
% 0.21/0.61 % Removed in clause preprocessing : 0
% 0.21/0.61 % Initial clauses in saturation : 17
% 0.21/0.61 % Processed clauses : 559
% 0.21/0.61 % ...of these trivial : 4
% 0.21/0.61 % ...subsumed : 344
% 0.21/0.61 % ...remaining for further processing : 211
% 0.21/0.61 % Other redundant clauses eliminated : 0
% 0.21/0.61 % Clauses deleted for lack of memory : 0
% 0.21/0.61 % Backward-subsumed : 3
% 0.21/0.61 % Backward-rewritten : 0
% 0.21/0.61 % Generated clauses : 1809
% 0.21/0.61 % ...of the previous two non-redundant : 1479
% 0.21/0.61 % ...aggressively subsumed : 0
% 0.21/0.61 % Contextual simplify-reflections : 0
% 0.21/0.61 % Paramodulations : 1809
% 0.21/0.61 % Factorizations : 0
% 0.21/0.61 % NegExts : 0
% 0.21/0.61 % Equation resolutions : 0
% 0.21/0.61 % Disequality decompositions : 0
% 0.21/0.61 % Total rewrite steps : 823
% 0.21/0.61 % ...of those cached : 807
% 0.21/0.61 % Propositional unsat checks : 0
% 0.21/0.61 % Propositional check models : 0
% 0.21/0.61 % Propositional check unsatisfiable : 0
% 0.21/0.61 % Propositional clauses : 0
% 0.21/0.61 % Propositional clauses after purity: 0
% 0.21/0.61 % Propositional unsat core size : 0
% 0.21/0.61 % Propositional preprocessing time : 0.000
% 0.21/0.61 % Propositional encoding time : 0.000
% 0.21/0.61 % Propositional solver time : 0.000
% 0.21/0.61 % Success case prop preproc time : 0.000
% 0.21/0.61 % Success case prop encoding time : 0.000
% 0.21/0.61 % Success case prop solver time : 0.000
% 0.21/0.61 % Current number of processed clauses : 208
% 0.21/0.61 % Positive orientable unit clauses : 17
% 0.21/0.61 % Positive unorientable unit clauses: 0
% 0.21/0.61 % Negative unit clauses : 3
% 0.21/0.61 % Non-unit-clauses : 188
% 0.21/0.61 % Current number of unprocessed clauses: 931
% 0.21/0.61 % ...number of literals in the above : 3528
% 0.21/0.61 % Current number of archived formulas : 0
% 0.21/0.61 % Current number of archived clauses : 3
% 0.21/0.61 % Clause-clause subsumption calls (NU) : 5636
% 0.21/0.61 % Rec. Clause-clause subsumption calls : 5419
% 0.21/0.61 % Non-unit clause-clause subsumptions : 347
% 0.21/0.61 % Unit Clause-clause subsumption calls : 14
% 0.21/0.61 % Rewrite failures with RHS unbound : 0
% 0.21/0.61 % BW rewrite match attempts : 12
% 0.21/0.61 % BW rewrite match successes : 0
% 0.21/0.61 % Condensation attempts : 0
% 0.21/0.61 % Condensation successes : 0
% 0.21/0.61 % Termbank termtop insertions : 26933
% 0.21/0.61 % Search garbage collected termcells : 142
% 0.21/0.61
% 0.21/0.61 % -------------------------------------------------
% 0.21/0.61 % User time : 0.031 s
% 0.21/0.61 % System time : 0.003 s
% 0.21/0.61 % Total time : 0.034 s
% 0.21/0.61 % Maximum resident set size: 3660 pages
% 0.21/0.61
% 0.21/0.61 % -------------------------------------------------
% 0.21/0.61 % User time : 0.033 s
% 0.21/0.61 % System time : 0.008 s
% 0.21/0.61 % Total time : 0.040 s
% 0.21/0.61 % Maximum resident set size: 4864 pages
% 0.21/0.61 % E exiting
%------------------------------------------------------------------------------