%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC256+1 : TPTP v9.3.1. Released v2.4.0.
% 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 02:43:41 PM UTC 2026
% Result : Theorem 0.13s 5.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 137 ( 50 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 163 ( 61 ~; 55 |; 20 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| singletonP(X1)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| singletonP(X1)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| singletonP(X1)
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_8,plain,
! [X45,X47] :
( ( ~ ssList(X45)
| singletonP(X45)
| cons(X47,nil) != X45
| ~ ssItem(X47) )
& ( ~ ssList(X45)
| ~ singletonP(X45)
| cons(esk12_1(X45),nil) = X45 )
& ( ~ ssList(X45)
| ~ singletonP(X45)
| ssItem(esk12_1(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])])]) ).
fof(c_0_9,negated_conjecture,
( ( memberP(esk4_0,esk5_0)
| nil = esk3_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_0 )
& ~ singletonP(esk1_0)
& neq(esk2_0,nil)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
inference(distribute,[status(thm)],[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_10,plain,
! [X15,X16] :
( nil != cons(X16,X15)
| ~ ssItem(X16)
| ~ ssList(X15) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
~ singletonP(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_15,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_18,negated_conjecture,
( ssItem(esk5_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
~ singletonP(esk3_0),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( ssItem(esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_24,plain,
! [X50,X51] :
( ( ~ ssList(X50)
| ~ ssList(X51)
| neq(X50,X51)
| X50 = X51 )
& ( ~ ssList(X50)
| ~ ssList(X51)
| X50 != X51
| ~ neq(X50,X51) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
cnf(c_0_25,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( esk3_0 != nil
| esk4_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = nil,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]),c_0_23]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
esk4_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC256+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 08:15:05 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.43 % Version: 3.5.1
% 0.13/5.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/5.43 % Starting sh5l with 300s (1) cores
% 0.13/5.43 % new_bool_3 with pid 2647896 completed with status 0
% 0.13/5.43 % Result found by new_bool_3
% 0.13/5.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/5.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/5.43 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/5.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/5.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/5.43 % SubtermCWHack with pid 2647899 completed with status 0
% 0.13/5.43 % Result found by SubtermCWHack
% 0.13/5.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/5.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/5.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/5.43 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/5.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/5.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/5.43 % Preprocessing time : 0.002 s
% 0.13/5.43
% 0.13/5.43 % Proof found!
% 0.13/5.43 % SZS status Theorem
% 0.13/5.43 % SZS output start CNFRefutation
% See solution above
% 0.13/5.43 % Parsed axioms : 96
% 0.13/5.43 % Removed by relevancy pruning/SinE : 71
% 0.13/5.43 % Initial clauses : 56
% 0.13/5.43 % Removed in clause preprocessing : 0
% 0.13/5.43 % Initial clauses in saturation : 56
% 0.13/5.43 % Processed clauses : 49
% 0.13/5.43 % ...of these trivial : 0
% 0.13/5.43 % ...subsumed : 4
% 0.13/5.43 % ...remaining for further processing : 45
% 0.13/5.43 % Other redundant clauses eliminated : 7
% 0.13/5.43 % Clauses deleted for lack of memory : 0
% 0.13/5.43 % Backward-subsumed : 0
% 0.13/5.43 % Backward-rewritten : 16
% 0.13/5.43 % Generated clauses : 22
% 0.13/5.43 % ...of the previous two non-redundant : 18
% 0.13/5.43 % ...aggressively subsumed : 0
% 0.13/5.43 % Contextual simplify-reflections : 2
% 0.13/5.43 % Paramodulations : 16
% 0.13/5.43 % Factorizations : 0
% 0.13/5.43 % NegExts : 0
% 0.13/5.43 % Equation resolutions : 7
% 0.13/5.43 % Disequality decompositions : 0
% 0.13/5.43 % Total rewrite steps : 42
% 0.13/5.43 % ...of those cached : 35
% 0.13/5.43 % Propositional unsat checks : 0
% 0.13/5.43 % Propositional check models : 0
% 0.13/5.43 % Propositional check unsatisfiable : 0
% 0.13/5.43 % Propositional clauses : 0
% 0.13/5.43 % Propositional clauses after purity: 0
% 0.13/5.43 % Propositional unsat core size : 0
% 0.13/5.43 % Propositional preprocessing time : 0.000
% 0.13/5.43 % Propositional encoding time : 0.000
% 0.13/5.43 % Propositional solver time : 0.000
% 0.13/5.43 % Success case prop preproc time : 0.000
% 0.13/5.43 % Success case prop encoding time : 0.000
% 0.13/5.43 % Success case prop solver time : 0.000
% 0.13/5.43 % Current number of processed clauses : 25
% 0.13/5.43 % Positive orientable unit clauses : 7
% 0.13/5.43 % Positive unorientable unit clauses: 0
% 0.13/5.43 % Negative unit clauses : 2
% 0.13/5.43 % Non-unit-clauses : 16
% 0.13/5.43 % Current number of unprocessed clauses: 24
% 0.13/5.43 % ...number of literals in the above : 100
% 0.13/5.43 % Current number of archived formulas : 0
% 0.13/5.43 % Current number of archived clauses : 16
% 0.13/5.43 % Clause-clause subsumption calls (NU) : 56
% 0.13/5.43 % Rec. Clause-clause subsumption calls : 21
% 0.13/5.43 % Non-unit clause-clause subsumptions : 3
% 0.13/5.43 % Unit Clause-clause subsumption calls : 2
% 0.13/5.43 % Rewrite failures with RHS unbound : 0
% 0.13/5.43 % BW rewrite match attempts : 4
% 0.13/5.43 % BW rewrite match successes : 4
% 0.13/5.43 % Condensation attempts : 0
% 0.13/5.43 % Condensation successes : 0
% 0.13/5.43 % Termbank termtop insertions : 5224
% 0.13/5.43 % Search garbage collected termcells : 1589
% 0.13/5.43
% 0.13/5.43 % -------------------------------------------------
% 0.13/5.43 % User time : 0.009 s
% 0.13/5.43 % System time : 0.002 s
% 0.13/5.43 % Total time : 0.011 s
% 0.13/5.43 % Maximum resident set size: 3756 pages
% 0.13/5.43
% 0.13/5.43 % -------------------------------------------------
% 0.13/5.43 % User time : 0.012 s
% 0.13/5.43 % System time : 0.004 s
% 0.13/5.43 % Total time : 0.016 s
% 0.13/5.43 % Maximum resident set size: 4864 pages
% 0.13/5.43 % E exiting
%------------------------------------------------------------------------------