%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:43:26 PM UTC 2026
% Result : Theorem 0.30s 0.66s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 140 ( 30 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 173 ( 68 ~; 63 |; 17 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| ~ singletonP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| ~ singletonP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,plain,
! [X125,X126] :
( hd(cons(X126,X125)) = X126
| ~ ssItem(X126)
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_8,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
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,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| ~ singletonP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_13,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
! [X255] :
( ( ~ ssItem(X255)
| X255 != esk52_1(X255) )
& ( ~ ssItem(X255)
| memberP(esk48_0,esk52_1(X255)) )
& ( ~ ssItem(X255)
| ssItem(esk52_1(X255)) )
& singletonP(esk50_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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)],[c_0_9])])])])])]) ).
cnf(c_0_15,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| esk5_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,negated_conjecture,
singletonP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_19,plain,
! [X154,X155,X156] :
( ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(cons(X155,X156),X154)
| ~ memberP(X156,X154) )
& ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(cons(X155,X156),X154)
| X154 != X155 )
& ( ~ ssItem(X154)
| ~ ssItem(X155)
| ~ ssList(X156)
| memberP(X156,X154)
| X154 = X155
| ~ memberP(cons(X155,X156),X154) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_20,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
singletonP(esk48_0),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(hd(X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
fof(c_0_24,plain,
! [X157] :
( ~ memberP(nil,X157)
| ~ ssItem(X157) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_25,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
cons(hd(esk48_0),nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
ssItem(hd(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22])]) ).
cnf(c_0_28,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk48_0,X1)
| hd(esk48_0) = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12]),c_0_27])]),c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssItem(X1)
| memberP(esk48_0,esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssItem(X1)
| ssItem(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( ~ ssItem(X1)
| X1 != esk52_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssItem(X1)
| esk52_1(X1) = hd(esk48_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33])]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n016.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 08:08:52 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 0.30/0.66 % Version: 3.5.1
% 0.30/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.66 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.66 % Starting sh5l with 300s (1) cores
% 0.30/0.66 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1974896 completed with status 0
% 0.30/0.66 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.30/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.66 % No SInE strategy applied
% 0.30/0.66 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.30/0.66 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.66 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.30/0.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.30/0.66 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.30/0.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.30/0.66 % SubtermCWHack with pid 1974903 completed with status 0
% 0.30/0.66 % Result found by SubtermCWHack
% 0.30/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.66 % No SInE strategy applied
% 0.30/0.66 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.30/0.66 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.66 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.66 % Preprocessing time : 0.005 s
% 0.30/0.66
% 0.30/0.66 % Proof found!
% 0.30/0.66 % SZS status Theorem
% 0.30/0.66 % SZS output start CNFRefutation
% See solution above
% 0.30/0.66 % Parsed axioms : 96
% 0.30/0.66 % Removed by relevancy pruning/SinE : 0
% 0.30/0.66 % Initial clauses : 200
% 0.30/0.66 % Removed in clause preprocessing : 2
% 0.30/0.66 % Initial clauses in saturation : 198
% 0.30/0.66 % Processed clauses : 481
% 0.30/0.66 % ...of these trivial : 4
% 0.30/0.66 % ...subsumed : 153
% 0.30/0.66 % ...remaining for further processing : 324
% 0.30/0.66 % Other redundant clauses eliminated : 65
% 0.30/0.66 % Clauses deleted for lack of memory : 0
% 0.30/0.66 % Backward-subsumed : 13
% 0.30/0.66 % Backward-rewritten : 19
% 0.30/0.66 % Generated clauses : 970
% 0.30/0.66 % ...of the previous two non-redundant : 685
% 0.30/0.66 % ...aggressively subsumed : 0
% 0.30/0.66 % Contextual simplify-reflections : 32
% 0.30/0.66 % Paramodulations : 901
% 0.30/0.66 % Factorizations : 0
% 0.30/0.66 % NegExts : 0
% 0.30/0.66 % Equation resolutions : 70
% 0.30/0.66 % Disequality decompositions : 0
% 0.30/0.66 % Total rewrite steps : 911
% 0.30/0.66 % ...of those cached : 881
% 0.30/0.66 % Propositional unsat checks : 0
% 0.30/0.66 % Propositional check models : 0
% 0.30/0.66 % Propositional check unsatisfiable : 0
% 0.30/0.66 % Propositional clauses : 0
% 0.30/0.66 % Propositional clauses after purity: 0
% 0.30/0.66 % Propositional unsat core size : 0
% 0.30/0.66 % Propositional preprocessing time : 0.000
% 0.30/0.66 % Propositional encoding time : 0.000
% 0.30/0.66 % Propositional solver time : 0.000
% 0.30/0.66 % Success case prop preproc time : 0.000
% 0.30/0.66 % Success case prop encoding time : 0.000
% 0.30/0.66 % Success case prop solver time : 0.000
% 0.30/0.66 % Current number of processed clauses : 278
% 0.30/0.66 % Positive orientable unit clauses : 40
% 0.30/0.66 % Positive unorientable unit clauses: 0
% 0.30/0.66 % Negative unit clauses : 6
% 0.30/0.66 % Non-unit-clauses : 232
% 0.30/0.66 % Current number of unprocessed clauses: 399
% 0.30/0.66 % ...number of literals in the above : 2280
% 0.30/0.66 % Current number of archived formulas : 0
% 0.30/0.66 % Current number of archived clauses : 32
% 0.30/0.66 % Clause-clause subsumption calls (NU) : 11019
% 0.30/0.66 % Rec. Clause-clause subsumption calls : 5412
% 0.30/0.66 % Non-unit clause-clause subsumptions : 165
% 0.30/0.66 % Unit Clause-clause subsumption calls : 85
% 0.30/0.66 % Rewrite failures with RHS unbound : 0
% 0.30/0.66 % BW rewrite match attempts : 11
% 0.30/0.66 % BW rewrite match successes : 11
% 0.30/0.66 % Condensation attempts : 0
% 0.30/0.66 % Condensation successes : 0
% 0.30/0.66 % Termbank termtop insertions : 32070
% 0.30/0.66 % Search garbage collected termcells : 4251
% 0.30/0.66
% 0.30/0.66 % -------------------------------------------------
% 0.30/0.66 % User time : 0.052 s
% 0.30/0.66 % System time : 0.009 s
% 0.30/0.66 % Total time : 0.061 s
% 0.30/0.66 % Maximum resident set size: 4012 pages
% 0.30/0.66
% 0.30/0.66 % -------------------------------------------------
% 0.30/0.66 % User time : 0.212 s
% 0.30/0.66 % System time : 0.032 s
% 0.30/0.66 % Total time : 0.244 s
% 0.30/0.66 % Maximum resident set size: 4864 pages
% 0.30/0.66 % E exiting
%------------------------------------------------------------------------------