%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD002-3 : 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 : n001.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 12:22:36 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 20 unt; 0 nHn; 41 RR)
% Number of literals : 81 ( 0 equ; 43 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(product_3,hypothesis,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_3) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_10,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_11,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_12,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_10 ).
cnf(c_0_13,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_14,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_15,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_11 ).
cnf(c_0_16,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_18,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
product(multiplicative_identity,a,b),
product_3 ).
cnf(c_0_20,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_21,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,hypothesis,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_23,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_24,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_25,hypothesis,
( ~ product(X1,a,a)
| product(X1,b,a) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_23 ).
cnf(c_0_27,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_28,hypothesis,
( ~ product(X1,a,a)
| product(b,X1,a) ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_29,hypothesis,
( ~ sum(X4,X3,b)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| sum(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,hypothesis,
product(b,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_32,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_33,negated_conjecture,
~ sum(additive_identity,a,b),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_34,hypothesis,
( ~ sum(X2,b,b)
| ~ product(X2,multiplicative_identity,X1)
| sum(X1,a,b) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_31 ).
cnf(c_0_36,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
~ sum(additive_identity,a,b),
c_0_33 ).
cnf(c_0_38,hypothesis,
( ~ product(additive_identity,multiplicative_identity,X1)
| sum(X1,a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_20])]) ).
cnf(c_0_39,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD002-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:41:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % new_bool_1 with pid 3484185 completed with status 0
% 0.14/0.46 % Result found by new_bool_1
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FHUNF-FFSS00-SFFFFFNN
% 0.14/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % SubtermCWHack with pid 3484187 completed with status 0
% 0.14/0.46 % Result found by SubtermCWHack
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FHUNF-FFSS00-SFFFFFNN
% 0.14/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % Preprocessing time : 0.001 s
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 30
% 0.14/0.46 % Removed by relevancy pruning/SinE : 13
% 0.14/0.46 % Initial clauses : 17
% 0.14/0.46 % Removed in clause preprocessing : 0
% 0.14/0.46 % Initial clauses in saturation : 17
% 0.14/0.46 % Processed clauses : 602
% 0.14/0.46 % ...of these trivial : 2
% 0.14/0.46 % ...subsumed : 315
% 0.14/0.46 % ...remaining for further processing : 285
% 0.14/0.46 % Other redundant clauses eliminated : 0
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 4
% 0.14/0.46 % Backward-rewritten : 0
% 0.14/0.46 % Generated clauses : 1329
% 0.14/0.46 % ...of the previous two non-redundant : 1062
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 1329
% 0.14/0.46 % Factorizations : 0
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 0
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 340
% 0.14/0.46 % ...of those cached : 323
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 281
% 0.14/0.46 % Positive orientable unit clauses : 18
% 0.14/0.46 % Positive unorientable unit clauses: 0
% 0.14/0.46 % Negative unit clauses : 2
% 0.14/0.46 % Non-unit-clauses : 261
% 0.14/0.46 % Current number of unprocessed clauses: 475
% 0.14/0.46 % ...number of literals in the above : 1876
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 4
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 8319
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 7888
% 0.14/0.46 % Non-unit clause-clause subsumptions : 319
% 0.14/0.46 % Unit Clause-clause subsumption calls : 0
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 5
% 0.14/0.46 % BW rewrite match successes : 0
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 18491
% 0.14/0.46 % Search garbage collected termcells : 149
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.032 s
% 0.14/0.46 % System time : 0.003 s
% 0.14/0.46 % Total time : 0.035 s
% 0.14/0.46 % Maximum resident set size: 3660 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.034 s
% 0.14/0.46 % System time : 0.007 s
% 0.14/0.46 % Total time : 0.042 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------