%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 03:14:19 PM UTC 2026
% Result : Theorem 7.79s 16.56s
% Output : CNFRefutation 7.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 74 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 33 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 98 ( 23 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_032,conjecture,
? [X11] : tc(nil,X11,arr(arr(a,arr(a,b)),arr(a,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
fof(axiom_029,axiom,
! [X1,X11,X12,X13] :
( tc(X1,lam(X11),arr(X12,X13))
<=> tc(cons(X12,X1),X11,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_027,axiom,
! [X1,X6,X9,X2,X10] :
( tc(X1,app(X9,X2,X10),X6)
<=> ( tc(X1,X2,X10)
& tc(X1,X9,arr(X10,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(axiom_031,axiom,
! [X1,X6,X3,X14] :
( index(X1,X3) = just(X14)
=> ( tc(X1,var(X3),X6)
<=> X14 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(axiom_025,axiom,
! [X6,X7] : index(cons(X6,X7),zero) = just(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(axiom_026,axiom,
! [X6,X7,X8] : index(cons(X6,X7),suc(X8)) = index(X7,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(c_0_6,negated_conjecture,
~ ? [X11] : tc(nil,X11,arr(arr(a,arr(a,b)),arr(a,b))),
inference(assume_negation,[status(cth)],[goal_032]) ).
fof(c_0_7,negated_conjecture,
! [X81] : ~ tc(nil,X81,arr(arr(a,arr(a,b)),arr(a,b))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X70,X71,X72,X73] :
( ( tc(X70,lam(X71),arr(X72,X73))
| ~ tc(cons(X72,X70),X71,X73) )
& ( tc(cons(X72,X70),X71,X73)
| ~ tc(X70,lam(X71),arr(X72,X73)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_029])])]) ).
cnf(c_0_9,negated_conjecture,
~ tc(nil,X1,arr(arr(a,arr(a,b)),arr(a,b))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ tc(cons(X1,X2),X3,X4)
| tc(X2,lam(X3),arr(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ tc(cons(arr(a,arr(a,b)),nil),X1,arr(a,b)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_12,plain,
! [X62,X63,X64,X65,X66] :
( ( tc(X62,app(X64,X65,X66),X63)
| ~ tc(X62,X65,X66)
| ~ tc(X62,X64,arr(X66,X63)) )
& ( ~ tc(X62,app(X64,X65,X66),X63)
| tc(X62,X65,X66) )
& ( ~ tc(X62,app(X64,X65,X66),X63)
| tc(X62,X64,arr(X66,X63)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_027])])])]) ).
cnf(c_0_13,negated_conjecture,
~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,b),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,plain,
( ~ tc(X1,X5,X3)
| ~ tc(X1,X2,arr(X3,X4))
| tc(X1,app(X2,X5,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X77,X78,X79,X80] :
( ( index(X77,X79) != just(X80)
| tc(X77,var(X79),X78)
| X80 != X78 )
& ( index(X77,X79) != just(X80)
| X80 = X78
| ~ tc(X77,var(X79),X78) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_031])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,arr(X2,b)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( index(X3,X4) != just(X1)
| X1 != X2
| tc(X3,var(X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_19,plain,
( index(X1,X2) != just(X3)
| tc(X1,var(X2),X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X3)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X5,X2)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X3)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
fof(c_0_22,plain,
! [X57,X58] : index(cons(X57,X58),zero) = just(X57),
inference(variable_rename,[status(thm)],[axiom_025]) ).
cnf(c_0_23,negated_conjecture,
( index(cons(a,cons(arr(a,arr(a,b)),nil)),X5) != just(X2)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X3)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_24,plain,
index(cons(X1,X2),zero) = just(X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( just(a) != just(X3)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X4) != just(X2)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_26,plain,
! [X59,X60,X61] : index(cons(X59,X60),suc(X61)) = index(X60,X61),
inference(variable_rename,[status(thm)],[axiom_026]) ).
cnf(c_0_27,negated_conjecture,
( just(a) != just(X3)
| just(a) != just(X2)
| index(cons(a,cons(arr(a,arr(a,b)),nil)),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_28,plain,
index(cons(X1,X2),suc(X3)) = index(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( just(a) != just(X3)
| just(a) != just(X2)
| index(cons(arr(a,arr(a,b)),nil),X1) != just(arr(X2,arr(X3,b))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( just(a) != just(X2)
| just(a) != just(X1)
| just(arr(a,arr(a,b))) != just(arr(X1,arr(X2,b))) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/15.45 % Computer : n008.cluster.edu
% 0.17/15.45 % Model : x86_64 x86_64
% 0.17/15.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.45 % Memory : 8046.5625MB
% 0.17/15.45 % OS : Linux 6.8.0-71-generic
% 0.17/15.45 % CPULimit : 300
% 0.17/15.45 % WCLimit : 300
% 0.17/15.45 % DateTime : Mon Sep 21 10:37:25 UTC 2026
% 0.17/15.46 % CPUTime :
% 0.17/15.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/15.53 Running first-order theorem proving
% 0.21/15.53 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
% 7.79/16.56 % Version: 3.5.1
% 7.79/16.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.79/16.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.79/16.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.79/16.56 % Starting new_bool_3 with 300s (1) cores
% 7.79/16.56 % Starting new_bool_1 with 300s (1) cores
% 7.79/16.56 % Starting sh5l with 300s (1) cores
% 7.79/16.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 767580 completed with status 0
% 7.79/16.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.79/16.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.79/16.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.79/16.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.79/16.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.79/16.56 % No SInE strategy applied
% 7.79/16.56 % Search class: FHHSM-FFMF31-MFFFFFNN
% 7.79/16.56 % partial match(1): FGHSM-FFMF31-MFFFFFNN
% 7.79/16.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.79/16.56 % Starting SubtermCWHack with 136s (1) cores
% 7.79/16.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.79/16.56 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 7.79/16.56 % Starting new_bool_3 with 136s (1) cores
% 7.79/16.56 % Starting new_bool_1 with 136s (1) cores
% 7.79/16.56 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with pid 767588 completed with status 0
% 7.79/16.56 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN
% 7.79/16.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.79/16.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.79/16.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.79/16.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.79/16.56 % No SInE strategy applied
% 7.79/16.56 % Search class: FHHSM-FFMF31-MFFFFFNN
% 7.79/16.56 % partial match(1): FGHSM-FFMF31-MFFFFFNN
% 7.79/16.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.79/16.56 % Starting SubtermCWHack with 136s (1) cores
% 7.79/16.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.79/16.56 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 7.79/16.56 % Preprocessing time : 0.006 s
% 7.79/16.56
% 7.79/16.56 % Proof found!
% 7.79/16.56 % SZS status Theorem
% 7.79/16.56 % SZS output start CNFRefutation
% See solution above
% 7.79/16.56 % Parsed axioms : 32
% 7.79/16.56 % Removed by relevancy pruning/SinE : 0
% 7.79/16.56 % Initial clauses : 36
% 7.79/16.56 % Removed in clause preprocessing : 0
% 7.79/16.56 % Initial clauses in saturation : 36
% 7.79/16.56 % Processed clauses : 988
% 7.79/16.56 % ...of these trivial : 0
% 7.79/16.56 % ...subsumed : 241
% 7.79/16.56 % ...remaining for further processing : 747
% 7.79/16.56 % Other redundant clauses eliminated : 1
% 7.79/16.56 % Clauses deleted for lack of memory : 0
% 7.79/16.56 % Backward-subsumed : 0
% 7.79/16.56 % Backward-rewritten : 0
% 7.79/16.56 % Generated clauses : 1723
% 7.79/16.56 % ...of the previous two non-redundant : 1717
% 7.79/16.56 % ...aggressively subsumed : 0
% 7.79/16.56 % Contextual simplify-reflections : 0
% 7.79/16.56 % Paramodulations : 1676
% 7.79/16.56 % Factorizations : 0
% 7.79/16.56 % NegExts : 0
% 7.79/16.56 % Equation resolutions : 47
% 7.79/16.56 % Disequality decompositions : 0
% 7.79/16.56 % Total rewrite steps : 284
% 7.79/16.56 % ...of those cached : 276
% 7.79/16.56 % Propositional unsat checks : 0
% 7.79/16.56 % Propositional check models : 0
% 7.79/16.56 % Propositional check unsatisfiable : 0
% 7.79/16.56 % Propositional clauses : 0
% 7.79/16.56 % Propositional clauses after purity: 0
% 7.79/16.56 % Propositional unsat core size : 0
% 7.79/16.56 % Propositional preprocessing time : 0.000
% 7.79/16.56 % Propositional encoding time : 0.000
% 7.79/16.56 % Propositional solver time : 0.000
% 7.79/16.56 % Success case prop preproc time : 0.000
% 7.79/16.56 % Success case prop encoding time : 0.000
% 7.79/16.56 % Success case prop solver time : 0.000
% 7.79/16.56 % Current number of processed clauses : 746
% 7.79/16.56 % Positive orientable unit clauses : 14
% 7.79/16.56 % Positive unorientable unit clauses: 0
% 7.79/16.56 % Negative unit clauses : 27
% 7.79/16.56 % Non-unit-clauses : 705
% 7.79/16.56 % Current number of unprocessed clauses: 765
% 7.79/16.56 % ...number of literals in the above : 10359
% 7.79/16.56 % Current number of archived formulas : 0
% 7.79/16.56 % Current number of archived clauses : 0
% 7.79/16.56 % Clause-clause subsumption calls (NU) : 1179972
% 7.79/16.56 % Rec. Clause-clause subsumption calls : 46227
% 7.79/16.56 % Non-unit clause-clause subsumptions : 82
% 7.79/16.56 % Unit Clause-clause subsumption calls : 798
% 7.79/16.56 % Rewrite failures with RHS unbound : 0
% 7.79/16.56 % BW rewrite match attempts : 0
% 7.79/16.56 % BW rewrite match successes : 0
% 7.79/16.56 % Condensation attempts : 0
% 7.79/16.56 % Condensation successes : 0
% 7.79/16.56 % Termbank termtop insertions : 113024
% 7.79/16.56 % Search garbage collected termcells : 232
% 7.79/16.56
% 7.79/16.56 % -------------------------------------------------
% 7.79/16.56 % User time : 0.971 s
% 7.79/16.56 % System time : 0.018 s
% 7.79/16.56 % Total time : 0.989 s
% 7.79/16.56 % Maximum resident set size: 3664 pages
% 7.79/16.56
% 7.79/16.56 % -------------------------------------------------
% 7.79/16.56 % User time : 4.717 s
% 7.79/16.56 % System time : 0.175 s
% 7.79/16.56 % Total time : 4.892 s
% 7.79/16.56 % Maximum resident set size: 4864 pages
% 7.79/16.56 % E exiting
%------------------------------------------------------------------------------