%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC331+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 : n013.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 02:43:58 PM UTC 2026
% Result : Theorem 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 123 ( 34 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 145 ( 49 ~; 45 |; 29 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 30 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( equalelemsP(X1)
& segmentP(X2,X1) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( equalelemsP(X1)
& segmentP(X2,X1) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| 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)
=> ( ( equalelemsP(X1)
& segmentP(X2,X1) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X3
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X39,X40,X41,X42] :
( segmentP(app(app(X41,X39),X42),X40)
| ~ segmentP(X39,X40)
| ~ ssList(X42)
| ~ ssList(X41)
| ~ ssList(X40)
| ~ ssList(X39) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_8,plain,
! [X55] :
( app(nil,X55) = X55
| ~ ssList(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_9,negated_conjecture,
! [X14,X15,X16] :
( ( ~ equalelemsP(esk1_0)
| ~ segmentP(esk2_0,esk1_0) )
& ( nil != esk3_0
| nil = esk4_0 )
& ( app(X16,cons(X14,nil)) != esk3_0
| ~ ssList(X16)
| app(cons(X14,nil),X15) != esk5_0
| ~ ssList(X15)
| ~ ssItem(X14) )
& equalelemsP(esk3_0)
& app(esk3_0,esk5_0) = esk4_0
& ssList(esk5_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
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_10,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ ssList(X1)
| app(nil,X1) = 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,negated_conjecture,
( ~ equalelemsP(esk1_0)
| ~ segmentP(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
equalelemsP(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_18,negated_conjecture,
app(esk3_0,esk5_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_14])]) ).
cnf(c_0_22,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk3_0,X1)
| segmentP(esk4_0,X1) ),
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_23,plain,
! [X38] :
( segmentP(X38,X38)
| ~ ssList(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_24,negated_conjecture,
~ segmentP(esk3_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20])]) ).
cnf(c_0_25,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC331+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 08:15:51 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.57 % Version: 3.5.1
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % Starting sh5l with 300s (1) cores
% 0.22/0.57 % new_bool_3 with pid 340536 completed with status 0
% 0.22/0.57 % Result found by new_bool_3
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % SubtermCWHack with pid 340539 completed with status 0
% 0.22/0.57 % Result found by SubtermCWHack
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % Preprocessing time : 0.002 s
% 0.22/0.57
% 0.22/0.57 % Proof found!
% 0.22/0.57 % SZS status Theorem
% 0.22/0.57 % SZS output start CNFRefutation
% See solution above
% 0.22/0.57 % Parsed axioms : 96
% 0.22/0.57 % Removed by relevancy pruning/SinE : 69
% 0.22/0.57 % Initial clauses : 55
% 0.22/0.57 % Removed in clause preprocessing : 0
% 0.22/0.57 % Initial clauses in saturation : 55
% 0.22/0.57 % Processed clauses : 293
% 0.22/0.57 % ...of these trivial : 23
% 0.22/0.57 % ...subsumed : 102
% 0.22/0.57 % ...remaining for further processing : 168
% 0.22/0.57 % Other redundant clauses eliminated : 17
% 0.22/0.57 % Clauses deleted for lack of memory : 0
% 0.22/0.57 % Backward-subsumed : 42
% 0.22/0.57 % Backward-rewritten : 2
% 0.22/0.57 % Generated clauses : 895
% 0.22/0.57 % ...of the previous two non-redundant : 717
% 0.22/0.57 % ...aggressively subsumed : 0
% 0.22/0.57 % Contextual simplify-reflections : 2
% 0.22/0.57 % Paramodulations : 875
% 0.22/0.57 % Factorizations : 0
% 0.22/0.57 % NegExts : 0
% 0.22/0.57 % Equation resolutions : 21
% 0.22/0.57 % Disequality decompositions : 0
% 0.22/0.57 % Total rewrite steps : 725
% 0.22/0.57 % ...of those cached : 708
% 0.22/0.57 % Propositional unsat checks : 0
% 0.22/0.57 % Propositional check models : 0
% 0.22/0.57 % Propositional check unsatisfiable : 0
% 0.22/0.57 % Propositional clauses : 0
% 0.22/0.57 % Propositional clauses after purity: 0
% 0.22/0.57 % Propositional unsat core size : 0
% 0.22/0.57 % Propositional preprocessing time : 0.000
% 0.22/0.57 % Propositional encoding time : 0.000
% 0.22/0.57 % Propositional solver time : 0.000
% 0.22/0.57 % Success case prop preproc time : 0.000
% 0.22/0.57 % Success case prop encoding time : 0.000
% 0.22/0.57 % Success case prop solver time : 0.000
% 0.22/0.57 % Current number of processed clauses : 120
% 0.22/0.57 % Positive orientable unit clauses : 17
% 0.22/0.57 % Positive unorientable unit clauses: 0
% 0.22/0.57 % Negative unit clauses : 6
% 0.22/0.57 % Non-unit-clauses : 97
% 0.22/0.57 % Current number of unprocessed clauses: 448
% 0.22/0.57 % ...number of literals in the above : 2314
% 0.22/0.57 % Current number of archived formulas : 0
% 0.22/0.57 % Current number of archived clauses : 44
% 0.22/0.57 % Clause-clause subsumption calls (NU) : 1462
% 0.22/0.57 % Rec. Clause-clause subsumption calls : 937
% 0.22/0.57 % Non-unit clause-clause subsumptions : 106
% 0.22/0.57 % Unit Clause-clause subsumption calls : 135
% 0.22/0.57 % Rewrite failures with RHS unbound : 0
% 0.22/0.57 % BW rewrite match attempts : 2
% 0.22/0.57 % BW rewrite match successes : 2
% 0.22/0.57 % Condensation attempts : 0
% 0.22/0.57 % Condensation successes : 0
% 0.22/0.57 % Termbank termtop insertions : 19008
% 0.22/0.57 % Search garbage collected termcells : 1676
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.024 s
% 0.22/0.57 % System time : 0.005 s
% 0.22/0.57 % Total time : 0.029 s
% 0.22/0.57 % Maximum resident set size: 3760 pages
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.031 s
% 0.22/0.57 % System time : 0.010 s
% 0.22/0.57 % Total time : 0.041 s
% 0.22/0.57 % Maximum resident set size: 4864 pages
% 0.22/0.57 % E exiting
%------------------------------------------------------------------------------