%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC313+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 : 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 02:43:54 PM UTC 2026
% Result : Theorem 0.23s 0.62s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 178 ( 84 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 222 ( 80 ~; 81 |; 40 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 28 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X7] :
( ? [X8] :
( app(X8,cons(X7,nil)) = X1
& app(cons(X7,nil),X8) = X2
& ssList(X8) )
& ssItem(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X7] :
( ? [X8] :
( app(X8,cons(X7,nil)) = X1
& app(cons(X7,nil),X8) = X2
& ssList(X8) )
& ssItem(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(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)
=> ( ( ( ? [X7] :
( ? [X8] :
( app(X8,cons(X7,nil)) = X1
& app(cons(X7,nil),X8) = X2
& ssList(X8) )
& ssItem(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X13,X14,X15,X16] :
( ( nil != esk1_0
| app(X16,cons(X15,nil)) != esk1_0
| app(cons(X15,nil),X16) != esk2_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| app(X16,cons(X15,nil)) != esk1_0
| app(cons(X15,nil),X16) != esk2_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( nil != esk4_0
| nil = esk3_0 )
& ( app(cons(X13,nil),X14) != esk4_0
| app(X14,cons(X13,nil)) = esk3_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& 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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( app(cons(X1,nil),X2) != esk4_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( app(X2,cons(X1,nil)) != esk1_0
| app(cons(X1,nil),X2) != esk2_0
| ~ ssList(X2)
| ~ ssItem(X1)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(cons(X2,nil),X1) != esk2_0
| app(X1,cons(X2,nil)) = esk1_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
fof(c_0_13,plain,
! [X29,X30] :
( cons(X30,X29) = app(cons(X30,nil),X29)
| ~ ssItem(X30)
| ~ ssList(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk2_0
| esk2_0 = nil ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X45] :
( ( ~ ssList(X45)
| nil = X45
| cons(esk6_1(X45),esk5_1(X45)) = X45 )
& ( ~ ssList(X45)
| nil = X45
| ssItem(esk6_1(X45)) )
& ( ~ ssList(X45)
| nil = X45
| ssList(esk5_1(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,X2) != esk2_0
| esk2_0 = nil ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( ~ ssItem(esk6_1(esk2_0))
| ~ ssList(esk5_1(esk2_0))
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]),c_0_19])]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_23,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssList(esk5_1(esk2_0))
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19])]) ).
cnf(c_0_25,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_26,plain,
! [X54,X55] :
( ( ~ ssList(X54)
| ~ ssList(X55)
| neq(X54,X55)
| X54 = X55 )
& ( ~ ssList(X54)
| ~ ssList(X55)
| X54 != X55
| ~ neq(X54,X55) ) ),
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_22])])])])]) ).
cnf(c_0_27,negated_conjecture,
( esk2_0 != nil
| esk1_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_9]),c_0_10]) ).
cnf(c_0_28,negated_conjecture,
esk2_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19])]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,negated_conjecture,
esk1_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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28]),c_0_31])]) ).
cnf(c_0_34,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC313+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % 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 08:17:18 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.55 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
% 0.23/0.62 % Version: 3.5.1
% 0.23/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.62 % Starting sh5l with 300s (1) cores
% 0.23/0.62 % new_bool_3 with pid 2847934 completed with status 0
% 0.23/0.62 % Result found by new_bool_3
% 0.23/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.62 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.23/0.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.62 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.62 % SubtermCWHack with pid 2847940 completed with status 0
% 0.23/0.62 % Result found by SubtermCWHack
% 0.23/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.23/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.62 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.23/0.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.62 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.62 % Preprocessing time : 0.003 s
% 0.23/0.62
% 0.23/0.62 % Proof found!
% 0.23/0.62 % SZS status Theorem
% 0.23/0.62 % SZS output start CNFRefutation
% See solution above
% 0.23/0.62 % Parsed axioms : 96
% 0.23/0.62 % Removed by relevancy pruning/SinE : 77
% 0.23/0.62 % Initial clauses : 39
% 0.23/0.62 % Removed in clause preprocessing : 0
% 0.23/0.62 % Initial clauses in saturation : 39
% 0.23/0.62 % Processed clauses : 87
% 0.23/0.62 % ...of these trivial : 0
% 0.23/0.62 % ...subsumed : 24
% 0.23/0.62 % ...remaining for further processing : 63
% 0.23/0.62 % Other redundant clauses eliminated : 13
% 0.23/0.62 % Clauses deleted for lack of memory : 0
% 0.23/0.62 % Backward-subsumed : 1
% 0.23/0.62 % Backward-rewritten : 15
% 0.23/0.62 % Generated clauses : 192
% 0.23/0.62 % ...of the previous two non-redundant : 149
% 0.23/0.62 % ...aggressively subsumed : 0
% 0.23/0.62 % Contextual simplify-reflections : 4
% 0.23/0.62 % Paramodulations : 176
% 0.23/0.62 % Factorizations : 0
% 0.23/0.62 % NegExts : 0
% 0.23/0.62 % Equation resolutions : 17
% 0.23/0.62 % Disequality decompositions : 0
% 0.23/0.62 % Total rewrite steps : 135
% 0.23/0.62 % ...of those cached : 127
% 0.23/0.62 % Propositional unsat checks : 0
% 0.23/0.62 % Propositional check models : 0
% 0.23/0.62 % Propositional check unsatisfiable : 0
% 0.23/0.62 % Propositional clauses : 0
% 0.23/0.62 % Propositional clauses after purity: 0
% 0.23/0.62 % Propositional unsat core size : 0
% 0.23/0.62 % Propositional preprocessing time : 0.000
% 0.23/0.62 % Propositional encoding time : 0.000
% 0.23/0.62 % Propositional solver time : 0.000
% 0.23/0.62 % Success case prop preproc time : 0.000
% 0.23/0.62 % Success case prop encoding time : 0.000
% 0.23/0.62 % Success case prop solver time : 0.000
% 0.23/0.62 % Current number of processed clauses : 44
% 0.23/0.62 % Positive orientable unit clauses : 9
% 0.23/0.62 % Positive unorientable unit clauses: 0
% 0.23/0.62 % Negative unit clauses : 1
% 0.23/0.62 % Non-unit-clauses : 34
% 0.23/0.62 % Current number of unprocessed clauses: 100
% 0.23/0.62 % ...number of literals in the above : 542
% 0.23/0.62 % Current number of archived formulas : 0
% 0.23/0.62 % Current number of archived clauses : 16
% 0.23/0.62 % Clause-clause subsumption calls (NU) : 399
% 0.23/0.62 % Rec. Clause-clause subsumption calls : 193
% 0.23/0.62 % Non-unit clause-clause subsumptions : 29
% 0.23/0.62 % Unit Clause-clause subsumption calls : 21
% 0.23/0.62 % Rewrite failures with RHS unbound : 0
% 0.23/0.62 % BW rewrite match attempts : 4
% 0.23/0.62 % BW rewrite match successes : 4
% 0.23/0.62 % Condensation attempts : 0
% 0.23/0.62 % Condensation successes : 0
% 0.23/0.62 % Termbank termtop insertions : 7191
% 0.23/0.62 % Search garbage collected termcells : 1395
% 0.23/0.62
% 0.23/0.62 % -------------------------------------------------
% 0.23/0.62 % User time : 0.019 s
% 0.23/0.62 % System time : 0.004 s
% 0.23/0.62 % Total time : 0.023 s
% 0.23/0.62 % Maximum resident set size: 3760 pages
% 0.23/0.62
% 0.23/0.62 % -------------------------------------------------
% 0.23/0.62 % User time : 0.026 s
% 0.23/0.62 % System time : 0.011 s
% 0.23/0.62 % Total time : 0.037 s
% 0.23/0.62 % Maximum resident set size: 4864 pages
% 0.23/0.62 % E exiting
%------------------------------------------------------------------------------