%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD031-5 : 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 : n018.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 12:23:14 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 18 unt; 8 nHn; 45 RR)
% Number of literals : 91 ( 0 equ; 44 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 57 ( 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(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(product_2,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
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_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
cnf(not_product_4,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_9,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_10,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_11,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_9 ).
cnf(c_0_12,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_13,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_14,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_10 ).
cnf(c_0_15,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_17,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
product_2 ).
cnf(c_0_19,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
product(a,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,hypothesis,
product(multiplicative_identity,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(a,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_26,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_27,negated_conjecture,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_28,hypothesis,
product(a,a,multiplicative_identity),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_29,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_30,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_3]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_26 ).
cnf(c_0_32,hypothesis,
( ~ product(X1,multiplicative_identity,multiplicative_identity)
| product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_33,hypothesis,
( ~ product(X1,a,multiplicative_identity)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_29 ).
cnf(c_0_35,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_30 ).
cnf(c_0_36,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_identity,multiplicative_inverse(X1),multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_37,hypothesis,
( ~ product(X1,multiplicative_identity,multiplicative_identity)
| product(a,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_38,hypothesis,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_12])]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(fof_simplification,[status(thm)],[not_product_4]) ).
cnf(c_0_40,plain,
( ~ defined(X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,multiplicative_inverse(X3),X2)
| sum(additive_identity,X3,additive_identity)
| product(X1,X2,multiplicative_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_36]) ).
cnf(c_0_41,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
c_0_39 ).
cnf(c_0_43,hypothesis,
( ~ product(X1,a,multiplicative_identity)
| product(X1,multiplicative_identity,multiplicative_inverse(a)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_12])]),c_0_35]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-5 : 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 : n018.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 15:41:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % new_bool_3 with pid 2242283 completed with status 0
% 0.11/0.44 % Result found by new_bool_3
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGUNF-FFSS11-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % SubtermCWHack with pid 2242292 completed with status 0
% 0.11/0.44 % Result found by SubtermCWHack
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.44 % Search class: FGUNF-FFSS11-SFFFFFNN
% 0.11/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Unsatisfiable
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 30
% 0.11/0.44 % Removed by relevancy pruning/SinE : 11
% 0.11/0.44 % Initial clauses : 19
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 19
% 0.11/0.44 % Processed clauses : 258
% 0.11/0.44 % ...of these trivial : 1
% 0.11/0.44 % ...subsumed : 86
% 0.11/0.44 % ...remaining for further processing : 171
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 0
% 0.11/0.44 % Generated clauses : 747
% 0.11/0.44 % ...of the previous two non-redundant : 544
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 747
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 237
% 0.11/0.44 % ...of those cached : 210
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 171
% 0.11/0.45 % Positive orientable unit clauses : 30
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 3
% 0.11/0.45 % Non-unit-clauses : 138
% 0.11/0.45 % Current number of unprocessed clauses: 305
% 0.11/0.45 % ...number of literals in the above : 1098
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 0
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 1340
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 1198
% 0.11/0.45 % Non-unit clause-clause subsumptions : 86
% 0.11/0.45 % Unit Clause-clause subsumption calls : 24
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 12
% 0.11/0.45 % BW rewrite match successes : 0
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 9740
% 0.11/0.45 % Search garbage collected termcells : 142
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.009 s
% 0.11/0.45 % System time : 0.003 s
% 0.11/0.45 % Total time : 0.012 s
% 0.11/0.45 % Maximum resident set size: 3660 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.010 s
% 0.11/0.45 % System time : 0.009 s
% 0.11/0.45 % Total time : 0.019 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------