%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC243+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 : n012.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 02:43:37 PM UTC 2026
% Result : Theorem 0.18s 0.55s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 6 unt; 0 def)
% Number of atoms : 175 ( 44 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 233 ( 94 ~; 88 |; 28 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 0 sgn 33 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ totalorderedP(X3)
| 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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ totalorderedP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_8,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X1
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| nil = X1
| ~ totalorderedP(X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
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_8])])]) ).
fof(c_0_11,negated_conjecture,
! [X257,X258,X259] :
( ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| ~ leq(X257,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| lt(X257,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| memberP(X259,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| memberP(X258,esk52_3(X257,X258,X259)) )
& ( ~ ssItem(X257)
| ~ ssList(X258)
| app(app(X258,cons(X257,nil)),X259) != esk48_0
| ~ ssList(X259)
| ssItem(esk52_3(X257,X258,X259)) )
& nil != esk48_0
& totalorderedP(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_12,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X3)
| memberP(X1,esk52_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_15,negated_conjecture,
( ~ ssItem(X1)
| ~ ssItem(esk52_3(X1,nil,X2))
| ~ ssList(X2)
| app(app(nil,cons(X1,nil)),X2) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_16,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X3)
| ssItem(esk52_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(app(nil,cons(X1,nil)),X2) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14])]) ).
cnf(c_0_19,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X222,X223] :
( cons(X223,X222) = app(cons(X223,nil),X222)
| ~ ssItem(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| app(cons(X1,nil),X2) != esk48_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X113,X114] :
( ssList(cons(X114,X113))
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| cons(X1,X2) != esk48_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X121] :
( ( ~ ssList(X121)
| nil = X121
| cons(esk45_1(X121),esk44_1(X121)) = X121 )
& ( ~ ssList(X121)
| nil = X121
| ssItem(esk45_1(X121)) )
& ( ~ ssList(X121)
| nil = X121
| ssList(esk44_1(X121)) ) ),
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_27,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,X2) != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14])]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssItem(esk45_1(esk48_0))
| ~ ssList(esk44_1(esk48_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28])]),c_0_29])]),c_0_30]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
~ ssList(esk44_1(esk48_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]),c_0_30]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC243+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.38 % Computer : n012.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Mon Sep 21 08:07:36 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.42 Running first-order theorem proving
% 0.08/0.42 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
% 0.18/0.55 % Version: 3.5.1
% 0.18/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.55 % Starting sh5l with 300s (1) cores
% 0.18/0.55 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1952749 completed with status 0
% 0.18/0.55 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.18/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.55 % No SInE strategy applied
% 0.18/0.55 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.18/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.18/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.18/0.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.18/0.55 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.18/0.55 % SAT001_MinMin_p005000_rr_RG with pid 1952758 completed with status 0
% 0.18/0.55 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.18/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.55 % No SInE strategy applied
% 0.18/0.55 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.18/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.18/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.18/0.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.18/0.55 % Preprocessing time : 0.004 s
% 0.18/0.55 % Presaturation interreduction done
% 0.18/0.55
% 0.18/0.55 % Proof found!
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 % SZS output start CNFRefutation
% See solution above
% 0.18/0.55 % Parsed axioms : 96
% 0.18/0.55 % Removed by relevancy pruning/SinE : 0
% 0.18/0.55 % Initial clauses : 203
% 0.18/0.55 % Removed in clause preprocessing : 2
% 0.18/0.55 % Initial clauses in saturation : 201
% 0.18/0.55 % Processed clauses : 626
% 0.18/0.55 % ...of these trivial : 2
% 0.18/0.55 % ...subsumed : 137
% 0.18/0.55 % ...remaining for further processing : 487
% 0.18/0.55 % Other redundant clauses eliminated : 99
% 0.18/0.55 % Clauses deleted for lack of memory : 0
% 0.18/0.55 % Backward-subsumed : 16
% 0.18/0.55 % Backward-rewritten : 2
% 0.18/0.55 % Generated clauses : 965
% 0.18/0.55 % ...of the previous two non-redundant : 783
% 0.18/0.55 % ...aggressively subsumed : 0
% 0.18/0.55 % Contextual simplify-reflections : 26
% 0.18/0.55 % Paramodulations : 862
% 0.18/0.55 % Factorizations : 0
% 0.18/0.55 % NegExts : 0
% 0.18/0.55 % Equation resolutions : 105
% 0.18/0.55 % Disequality decompositions : 0
% 0.18/0.55 % Total rewrite steps : 378
% 0.18/0.55 % ...of those cached : 366
% 0.18/0.55 % Propositional unsat checks : 0
% 0.18/0.55 % Propositional check models : 0
% 0.18/0.55 % Propositional check unsatisfiable : 0
% 0.18/0.55 % Propositional clauses : 0
% 0.18/0.55 % Propositional clauses after purity: 0
% 0.18/0.55 % Propositional unsat core size : 0
% 0.18/0.55 % Propositional preprocessing time : 0.000
% 0.18/0.55 % Propositional encoding time : 0.000
% 0.18/0.55 % Propositional solver time : 0.000
% 0.18/0.55 % Success case prop preproc time : 0.000
% 0.18/0.55 % Success case prop encoding time : 0.000
% 0.18/0.55 % Success case prop solver time : 0.000
% 0.18/0.55 % Current number of processed clauses : 251
% 0.18/0.55 % Positive orientable unit clauses : 21
% 0.18/0.55 % Positive unorientable unit clauses: 0
% 0.18/0.55 % Negative unit clauses : 5
% 0.18/0.55 % Non-unit-clauses : 225
% 0.18/0.55 % Current number of unprocessed clauses: 550
% 0.18/0.55 % ...number of literals in the above : 3566
% 0.18/0.55 % Current number of archived formulas : 0
% 0.18/0.55 % Current number of archived clauses : 213
% 0.18/0.55 % Clause-clause subsumption calls (NU) : 24525
% 0.18/0.55 % Rec. Clause-clause subsumption calls : 5749
% 0.18/0.55 % Non-unit clause-clause subsumptions : 141
% 0.18/0.55 % Unit Clause-clause subsumption calls : 65
% 0.18/0.55 % Rewrite failures with RHS unbound : 0
% 0.18/0.55 % BW rewrite match attempts : 2
% 0.18/0.55 % BW rewrite match successes : 2
% 0.18/0.55 % Condensation attempts : 0
% 0.18/0.55 % Condensation successes : 0
% 0.18/0.55 % Termbank termtop insertions : 36339
% 0.18/0.55 % Search garbage collected termcells : 4354
% 0.18/0.55
% 0.18/0.55 % -------------------------------------------------
% 0.18/0.55 % User time : 0.056 s
% 0.18/0.55 % System time : 0.009 s
% 0.18/0.55 % Total time : 0.065 s
% 0.18/0.55 % Maximum resident set size: 4016 pages
% 0.18/0.55
% 0.18/0.55 % -------------------------------------------------
% 0.18/0.55 % User time : 0.278 s
% 0.18/0.55 % System time : 0.033 s
% 0.18/0.55 % Total time : 0.311 s
% 0.18/0.55 % Maximum resident set size: 4864 pages
% 0.18/0.55 % E exiting
%------------------------------------------------------------------------------