%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC198+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 : n019.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 02:43:25 PM UTC 2026
% Result : Theorem 0.24s 0.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 164 ( 53 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 205 ( 71 ~; 71 |; 39 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 29 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax2,axiom,
? [X1] :
( ? [X2] :
( X1 != X2
& ssItem(X2) )
& ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| 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 )
& ! [X7] :
( ssItem(X7)
=> ( ? [X8] :
( leq(X7,X8)
& memberP(X4,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X4,X7)
| cons(X7,nil) != X3 ) ) )
| ? [X5] :
( ! [X6] :
( ssItem(X6)
=> ( X5 = X6
| ~ memberP(X1,X6) ) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_8,plain,
! [X156,X157,X158] :
( ( ~ ssItem(X156)
| ~ ssItem(X157)
| ~ ssList(X158)
| memberP(cons(X157,X158),X156)
| ~ memberP(X158,X156) )
& ( ~ ssItem(X156)
| ~ ssItem(X157)
| ~ ssList(X158)
| memberP(cons(X157,X158),X156)
| X156 != X157 )
& ( ~ ssItem(X156)
| ~ ssItem(X157)
| ~ ssList(X158)
| memberP(X158,X156)
| X156 = X157
| ~ memberP(cons(X157,X158),X156) ) ),
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])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X257,X260] :
( ( ~ leq(esk53_0,X260)
| ~ memberP(esk51_0,X260)
| esk53_0 = X260
| ~ ssItem(X260)
| nil = esk50_0 )
& ( ~ leq(esk53_0,X260)
| ~ memberP(esk51_0,X260)
| esk53_0 = X260
| ~ ssItem(X260)
| nil = esk51_0 )
& ( memberP(esk51_0,esk53_0)
| nil = esk50_0 )
& ( memberP(esk51_0,esk53_0)
| nil = esk51_0 )
& ( cons(esk53_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk53_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssItem(esk53_0)
| nil = esk50_0 )
& ( ssItem(esk53_0)
| nil = esk51_0 )
& ( ~ ssItem(X257)
| X257 != esk52_1(X257) )
& ( ~ ssItem(X257)
| memberP(esk48_0,esk52_1(X257)) )
& ( ~ ssItem(X257)
| ssItem(esk52_1(X257)) )
& 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_6])])])])])]) ).
fof(c_0_10,plain,
! [X159] :
( ~ memberP(nil,X159)
| ~ ssItem(X159) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( cons(esk53_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_14,negated_conjecture,
( ssItem(esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssItem(X1)
| memberP(esk48_0,esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk50_0,X1)
| esk53_0 = X1
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ ssItem(X1)
| memberP(esk50_0,esk52_1(X1)) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ ssItem(X1)
| ssItem(esk52_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssItem(X1)
| X1 != esk52_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssItem(X1)
| esk50_0 = nil
| esk52_1(X1) = esk53_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
fof(c_0_23,plain,
? [X1] :
( ? [X2] :
( X1 != X2
& ssItem(X2) )
& ssItem(X1) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
cnf(c_0_24,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]),c_0_14]) ).
fof(c_0_25,plain,
( esk1_0 != esk2_0
& ssItem(esk2_0)
& ssItem(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_23])])]) ).
cnf(c_0_26,negated_conjecture,
( ~ ssItem(X1)
| memberP(nil,esk52_1(X1)) ),
inference(rw,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_27,plain,
ssItem(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
~ ssItem(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_26]),c_0_20]) ).
cnf(c_0_29,plain,
$false,
inference(sr,[status(thm)],[c_0_27,c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC198+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n019.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 08:04:05 UTC 2026
% 0.19/0.41 % CPUTime :
% 0.19/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 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
% 0.24/0.60 % Version: 3.5.1
% 0.24/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.60 % Starting sh5l with 300s (1) cores
% 0.24/0.60 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2095050 completed with status 0
% 0.24/0.60 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.24/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.60 % No SInE strategy applied
% 0.24/0.60 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.24/0.60 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/0.60 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.24/0.60 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.24/0.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.24/0.60 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 2095059 completed with status 0
% 0.24/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.24/0.60 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.60 % No SInE strategy applied
% 0.24/0.60 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.24/0.60 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.60 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/0.60 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.24/0.60 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.24/0.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.24/0.60 % Preprocessing time : 0.004 s
% 0.24/0.60 % Presaturation interreduction done
% 0.24/0.60
% 0.24/0.60 % Proof found!
% 0.24/0.60 % SZS status Theorem
% 0.24/0.60 % SZS output start CNFRefutation
% See solution above
% 0.24/0.60 % Parsed axioms : 96
% 0.24/0.60 % Removed by relevancy pruning/SinE : 0
% 0.24/0.60 % Initial clauses : 207
% 0.24/0.60 % Removed in clause preprocessing : 2
% 0.24/0.60 % Initial clauses in saturation : 205
% 0.24/0.60 % Processed clauses : 522
% 0.24/0.60 % ...of these trivial : 7
% 0.24/0.60 % ...subsumed : 49
% 0.24/0.60 % ...remaining for further processing : 466
% 0.24/0.60 % Other redundant clauses eliminated : 74
% 0.24/0.60 % Clauses deleted for lack of memory : 0
% 0.24/0.60 % Backward-subsumed : 69
% 0.24/0.60 % Backward-rewritten : 45
% 0.24/0.60 % Generated clauses : 976
% 0.24/0.60 % ...of the previous two non-redundant : 810
% 0.24/0.60 % ...aggressively subsumed : 0
% 0.24/0.60 % Contextual simplify-reflections : 32
% 0.24/0.60 % Paramodulations : 897
% 0.24/0.60 % Factorizations : 0
% 0.24/0.60 % NegExts : 0
% 0.24/0.60 % Equation resolutions : 79
% 0.24/0.60 % Disequality decompositions : 0
% 0.24/0.60 % Total rewrite steps : 398
% 0.24/0.60 % ...of those cached : 379
% 0.24/0.60 % Propositional unsat checks : 0
% 0.24/0.60 % Propositional check models : 0
% 0.24/0.60 % Propositional check unsatisfiable : 0
% 0.24/0.60 % Propositional clauses : 0
% 0.24/0.60 % Propositional clauses after purity: 0
% 0.24/0.60 % Propositional unsat core size : 0
% 0.24/0.60 % Propositional preprocessing time : 0.000
% 0.24/0.60 % Propositional encoding time : 0.000
% 0.24/0.60 % Propositional solver time : 0.000
% 0.24/0.60 % Success case prop preproc time : 0.000
% 0.24/0.60 % Success case prop encoding time : 0.000
% 0.24/0.60 % Success case prop solver time : 0.000
% 0.24/0.60 % Current number of processed clauses : 128
% 0.24/0.60 % Positive orientable unit clauses : 18
% 0.24/0.60 % Positive unorientable unit clauses: 0
% 0.24/0.60 % Negative unit clauses : 3
% 0.24/0.60 % Non-unit-clauses : 107
% 0.24/0.60 % Current number of unprocessed clauses: 690
% 0.24/0.60 % ...number of literals in the above : 4959
% 0.24/0.60 % Current number of archived formulas : 0
% 0.24/0.60 % Current number of archived clauses : 315
% 0.24/0.60 % Clause-clause subsumption calls (NU) : 20041
% 0.24/0.60 % Rec. Clause-clause subsumption calls : 4818
% 0.24/0.60 % Non-unit clause-clause subsumptions : 80
% 0.24/0.60 % Unit Clause-clause subsumption calls : 167
% 0.24/0.60 % Rewrite failures with RHS unbound : 0
% 0.24/0.60 % BW rewrite match attempts : 4
% 0.24/0.60 % BW rewrite match successes : 4
% 0.24/0.60 % Condensation attempts : 0
% 0.24/0.60 % Condensation successes : 0
% 0.24/0.60 % Termbank termtop insertions : 38970
% 0.24/0.60 % Search garbage collected termcells : 4377
% 0.24/0.60
% 0.24/0.60 % -------------------------------------------------
% 0.24/0.60 % User time : 0.071 s
% 0.24/0.60 % System time : 0.004 s
% 0.24/0.60 % Total time : 0.075 s
% 0.24/0.60 % Maximum resident set size: 4272 pages
% 0.24/0.60
% 0.24/0.60 % -------------------------------------------------
% 0.24/0.60 % User time : 0.216 s
% 0.24/0.60 % System time : 0.027 s
% 0.24/0.60 % Total time : 0.243 s
% 0.24/0.60 % Maximum resident set size: 4864 pages
% 0.24/0.60 % E exiting
%------------------------------------------------------------------------------