%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE007+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 : n004.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 12:58:33 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 56 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 50 ( 20 ~; 15 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 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(X4)
& test(X5) )
=> one = addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))) ),
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(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_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_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(c_0_6,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> one = addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X30,X31] :
( ( ~ test(X30)
| c(X30) = X31
| ~ complement(X30,X31) )
& ( ~ test(X30)
| complement(X30,X31)
| c(X30) != X31 ) ),
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,
( one != addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0)))
& test(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,
! [X15,X16,X17] : multiplication(X15,addition(X16,X17)) = addition(multiplication(X15,X16),multiplication(X15,X17)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_10,plain,
! [X21,X22] :
( ( complement(X22,X21)
| addition(X21,X22) != one
| multiplication(X22,X21) != zero
| multiplication(X21,X22) != zero )
& ( ~ complement(X22,X21)
| addition(X21,X22) = one )
& ( ~ complement(X22,X21)
| multiplication(X22,X21) = zero )
& ( ~ complement(X22,X21)
| multiplication(X21,X22) = 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,
one != addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,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,
! [X26] : multiplication(X26,one) = X26,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_19,negated_conjecture,
multiplication(addition(esk1_0,c(esk1_0)),addition(esk2_0,c(esk2_0))) != one,
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(X1,one) = 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,
addition(esk1_0,c(esk1_0)) != one,
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])]) ).
cnf(c_0_24,negated_conjecture,
test(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE007+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:37:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % sh5l with pid 1642517 completed with status 0
% 0.14/0.43 % Result found by sh5l
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.43 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 1642521 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.43 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 17
% 0.14/0.43 % Removed by relevancy pruning/SinE : 1
% 0.14/0.43 % Initial clauses : 23
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 23
% 0.14/0.43 % Processed clauses : 100
% 0.14/0.43 % ...of these trivial : 12
% 0.14/0.43 % ...subsumed : 15
% 0.14/0.43 % ...remaining for further processing : 73
% 0.14/0.43 % Other redundant clauses eliminated : 1
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 0
% 0.14/0.43 % Backward-rewritten : 0
% 0.14/0.43 % Generated clauses : 446
% 0.14/0.43 % ...of the previous two non-redundant : 188
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 1
% 0.14/0.43 % Paramodulations : 445
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 1
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 510
% 0.14/0.43 % ...of those cached : 357
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 72
% 0.14/0.43 % Positive orientable unit clauses : 34
% 0.14/0.43 % Positive unorientable unit clauses: 1
% 0.14/0.43 % Negative unit clauses : 2
% 0.14/0.43 % Non-unit-clauses : 35
% 0.14/0.43 % Current number of unprocessed clauses: 111
% 0.14/0.43 % ...number of literals in the above : 189
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 0
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 205
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 187
% 0.14/0.43 % Non-unit clause-clause subsumptions : 16
% 0.14/0.43 % Unit Clause-clause subsumption calls : 21
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 11
% 0.14/0.43 % BW rewrite match successes : 4
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 4750
% 0.14/0.43 % Search garbage collected termcells : 161
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.008 s
% 0.14/0.43 % System time : 0.001 s
% 0.14/0.43 % Total time : 0.009 s
% 0.14/0.43 % Maximum resident set size: 3648 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.011 s
% 0.14/0.43 % System time : 0.005 s
% 0.14/0.43 % Total time : 0.016 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------