%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE021+1 : TPTP v9.3.1. Released v4.0.0.
% 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 12:58:37 PM UTC 2026
% Result : Theorem 0.25s 0.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 51 ( 29 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 46 ( 19 ~; 15 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( test(X5)
=> X4 = addition(multiplication(X5,X4),multiplication(c(X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_6,negated_conjecture,
~ ! [X4,X5] :
( test(X5)
=> X4 = addition(multiplication(X5,X4),multiplication(c(X5),X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X23,X24] :
( ( ~ test(X23)
| c(X23) = X24
| ~ complement(X23,X24) )
& ( ~ test(X23)
| complement(X23,X24)
| c(X23) != X24 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_8,negated_conjecture,
( esk1_0 != addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0))
& test(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X17,X18,X19] : multiplication(addition(X17,X18),X19) = addition(multiplication(X17,X19),multiplication(X18,X19)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_10,plain,
! [X30,X31] :
( ( complement(X31,X30)
| addition(X30,X31) != one
| multiplication(X31,X30) != zero
| multiplication(X30,X31) != zero )
& ( ~ complement(X31,X30)
| addition(X30,X31) = one )
& ( ~ complement(X31,X30)
| multiplication(X31,X30) = zero )
& ( ~ complement(X31,X30)
| multiplication(X30,X31) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_11,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X8,X9] : addition(X8,X9) = addition(X9,X8),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_13,negated_conjecture,
esk1_0 != addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X36] : multiplication(one,X36) = X36,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_19,negated_conjecture,
multiplication(addition(esk2_0,c(esk2_0)),esk1_0) != esk1_0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n018.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 20 22:41:13 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.56 Running first-order theorem proving
% 0.25/0.56 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
% 0.25/0.62 % Version: 3.5.1
% 0.25/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.62 % Starting sh5l with 300s (1) cores
% 0.25/0.62 % new_bool_1 with pid 351533 completed with status 0
% 0.25/0.62 % Result found by new_bool_1
% 0.25/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.62 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.25/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.62 % SubtermCWHack with pid 351539 completed with status 0
% 0.25/0.62 % Result found by SubtermCWHack
% 0.25/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.62 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.25/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.62 % Preprocessing time : 0.001 s
% 0.25/0.62
% 0.25/0.62 % Proof found!
% 0.25/0.62 % SZS status Theorem
% 0.25/0.62 % SZS output start CNFRefutation
% See solution above
% 0.25/0.63 % Parsed axioms : 17
% 0.25/0.63 % Removed by relevancy pruning/SinE : 1
% 0.25/0.63 % Initial clauses : 22
% 0.25/0.63 % Removed in clause preprocessing : 0
% 0.25/0.63 % Initial clauses in saturation : 22
% 0.25/0.63 % Processed clauses : 89
% 0.25/0.63 % ...of these trivial : 7
% 0.25/0.63 % ...subsumed : 18
% 0.25/0.63 % ...remaining for further processing : 64
% 0.25/0.63 % Other redundant clauses eliminated : 1
% 0.25/0.63 % Clauses deleted for lack of memory : 0
% 0.25/0.63 % Backward-subsumed : 0
% 0.25/0.63 % Backward-rewritten : 1
% 0.25/0.63 % Generated clauses : 368
% 0.25/0.63 % ...of the previous two non-redundant : 164
% 0.25/0.63 % ...aggressively subsumed : 0
% 0.25/0.63 % Contextual simplify-reflections : 1
% 0.25/0.63 % Paramodulations : 367
% 0.25/0.63 % Factorizations : 0
% 0.25/0.63 % NegExts : 0
% 0.25/0.63 % Equation resolutions : 1
% 0.25/0.63 % Disequality decompositions : 0
% 0.25/0.63 % Total rewrite steps : 392
% 0.25/0.63 % ...of those cached : 259
% 0.25/0.63 % Propositional unsat checks : 0
% 0.25/0.63 % Propositional check models : 0
% 0.25/0.63 % Propositional check unsatisfiable : 0
% 0.25/0.63 % Propositional clauses : 0
% 0.25/0.63 % Propositional clauses after purity: 0
% 0.25/0.63 % Propositional unsat core size : 0
% 0.25/0.63 % Propositional preprocessing time : 0.000
% 0.25/0.63 % Propositional encoding time : 0.000
% 0.25/0.63 % Propositional solver time : 0.000
% 0.25/0.63 % Success case prop preproc time : 0.000
% 0.25/0.63 % Success case prop encoding time : 0.000
% 0.25/0.63 % Success case prop solver time : 0.000
% 0.25/0.63 % Current number of processed clauses : 62
% 0.25/0.63 % Positive orientable unit clauses : 25
% 0.25/0.63 % Positive unorientable unit clauses: 1
% 0.25/0.63 % Negative unit clauses : 1
% 0.25/0.63 % Non-unit-clauses : 35
% 0.25/0.63 % Current number of unprocessed clauses: 97
% 0.25/0.63 % ...number of literals in the above : 168
% 0.25/0.63 % Current number of archived formulas : 0
% 0.25/0.63 % Current number of archived clauses : 1
% 0.25/0.63 % Clause-clause subsumption calls (NU) : 146
% 0.25/0.63 % Rec. Clause-clause subsumption calls : 143
% 0.25/0.63 % Non-unit clause-clause subsumptions : 19
% 0.25/0.63 % Unit Clause-clause subsumption calls : 5
% 0.25/0.63 % Rewrite failures with RHS unbound : 0
% 0.25/0.63 % BW rewrite match attempts : 11
% 0.25/0.63 % BW rewrite match successes : 5
% 0.25/0.63 % Condensation attempts : 0
% 0.25/0.63 % Condensation successes : 0
% 0.25/0.63 % Termbank termtop insertions : 4038
% 0.25/0.63 % Search garbage collected termcells : 148
% 0.25/0.63
% 0.25/0.63 % -------------------------------------------------
% 0.25/0.63 % User time : 0.012 s
% 0.25/0.63 % System time : 0.003 s
% 0.25/0.63 % Total time : 0.015 s
% 0.25/0.63 % Maximum resident set size: 3648 pages
% 0.25/0.63
% 0.25/0.63 % -------------------------------------------------
% 0.25/0.63 % User time : 0.015 s
% 0.25/0.63 % System time : 0.008 s
% 0.25/0.63 % Total time : 0.024 s
% 0.25/0.63 % Maximum resident set size: 4608 pages
% 0.25/0.63 % E exiting
%------------------------------------------------------------------------------