%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE004+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 : n002.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 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 22 unt; 0 def)
% Number of atoms : 60 ( 34 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 51 ( 22 ~; 18 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 3 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(goals,conjecture,
c(zero) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(c_0_8,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_9,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_10,plain,
! [X32,X33] :
( ( complement(X33,X32)
| addition(X32,X33) != one
| multiplication(X33,X32) != zero
| multiplication(X32,X33) != zero )
& ( ~ complement(X33,X32)
| addition(X32,X33) = one )
& ( ~ complement(X33,X32)
| multiplication(X33,X32) = zero )
& ( ~ complement(X33,X32)
| multiplication(X32,X33) = 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,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_14,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_15,negated_conjecture,
c(zero) != one,
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_16,plain,
! [X28,X30,X31] :
( ( test(X30)
| ~ complement(X31,X30) )
& ( complement(esk1_1(X28),X28)
| ~ test(X28) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
cnf(c_0_17,plain,
( addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,negated_conjecture,
c(zero) != one,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X34,X35] :
( ( ~ test(X34)
| c(X34) = X35
| ~ complement(X34,X35) )
& ( ~ test(X34)
| complement(X34,X35)
| c(X34) != X35 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
cnf(c_0_23,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
complement(one,zero),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])])]) ).
fof(c_0_25,negated_conjecture,
c(zero) != one,
inference(fof_nnf,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
complement(zero,one),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_20]),c_0_19])])]) ).
cnf(c_0_28,plain,
test(zero),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
c(zero) != one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 22:40:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1856185 completed with status 0
% 0.12/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FGUSM-FFSF21-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.44 % new_bool_3 with pid 1856195 completed with status 0
% 0.12/0.44 % Result found by new_bool_3
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FGUSM-FFSF21-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44 % Presaturation interreduction done
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 17
% 0.12/0.44 % Removed by relevancy pruning/SinE : 0
% 0.12/0.44 % Initial clauses : 23
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 23
% 0.12/0.44 % Processed clauses : 58
% 0.12/0.44 % ...of these trivial : 1
% 0.12/0.44 % ...subsumed : 0
% 0.12/0.44 % ...remaining for further processing : 57
% 0.12/0.44 % Other redundant clauses eliminated : 5
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 2
% 0.12/0.44 % Generated clauses : 98
% 0.12/0.44 % ...of the previous two non-redundant : 49
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 1
% 0.12/0.44 % Paramodulations : 93
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 5
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 89
% 0.12/0.44 % ...of those cached : 37
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 31
% 0.12/0.44 % Positive orientable unit clauses : 17
% 0.12/0.44 % Positive unorientable unit clauses: 1
% 0.12/0.44 % Negative unit clauses : 1
% 0.12/0.44 % Non-unit-clauses : 12
% 0.12/0.44 % Current number of unprocessed clauses: 37
% 0.12/0.44 % ...number of literals in the above : 66
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 25
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 21
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 19
% 0.12/0.44 % Non-unit clause-clause subsumptions : 1
% 0.12/0.44 % Unit Clause-clause subsumption calls : 10
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 26
% 0.12/0.44 % BW rewrite match successes : 20
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 1842
% 0.12/0.44 % Search garbage collected termcells : 136
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.006 s
% 0.12/0.44 % System time : 0.004 s
% 0.12/0.44 % Total time : 0.010 s
% 0.12/0.44 % Maximum resident set size: 3648 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.025 s
% 0.12/0.44 % System time : 0.016 s
% 0.12/0.44 % Total time : 0.042 s
% 0.12/0.44 % Maximum resident set size: 4864 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------