%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX222+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 : n014.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 03:14:18 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 53 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 26 ~; 18 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_036,conjecture,
? [X7] :
( tc(nil,X7,arr(a,arr(b,b)))
& nf(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(axiom_033,axiom,
! [X1,X7,X12,X13] :
( tc(X1,lam(X7),arr(X12,X13))
<=> tc(cons(X12,X1),X7,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
fof(axiom_035,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_035) ).
fof(axiom_029,axiom,
! [X6,X8] : index(cons(X6,X8),zero) = just(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_026,axiom,
! [X7] :
( nf(lam(X7))
<=> nf(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_027,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(c_0_6,negated_conjecture,
~ ? [X7] :
( tc(nil,X7,arr(a,arr(b,b)))
& nf(X7) ),
inference(assume_negation,[status(cth)],[goal_036]) ).
fof(c_0_7,negated_conjecture,
! [X89] :
( ~ tc(nil,X89,arr(a,arr(b,b)))
| ~ nf(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X78,X79,X80,X81] :
( ( tc(X78,lam(X79),arr(X80,X81))
| ~ tc(cons(X80,X78),X79,X81) )
& ( tc(cons(X80,X78),X79,X81)
| ~ tc(X78,lam(X79),arr(X80,X81)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_033])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ tc(nil,X1,arr(a,arr(b,b)))
| ~ nf(X1) ),
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]) ).
fof(c_0_11,plain,
! [X85,X86,X87,X88] :
( ( index(X85,X87) != just(X88)
| tc(X85,var(X87),X86)
| X88 != X86 )
& ( index(X85,X87) != just(X88)
| X88 = X86
| ~ tc(X85,var(X87),X86) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_035])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ nf(lam(X1))
| ~ tc(cons(a,nil),X1,arr(b,b)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( index(X3,X4) != just(X1)
| X1 != X2
| tc(X3,var(X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( ~ nf(lam(lam(X1)))
| ~ tc(cons(b,cons(a,nil)),X1,b) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
( index(X1,X2) != just(X3)
| tc(X1,var(X2),X3) ),
inference(er,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X65,X66] : index(cons(X65,X66),zero) = just(X65),
inference(variable_rename,[status(thm)],[axiom_029]) ).
cnf(c_0_17,negated_conjecture,
( ~ nf(lam(lam(var(X1))))
| index(cons(b,cons(a,nil)),X1) != just(b) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
index(cons(X1,X2),zero) = just(X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X62] :
( ( nf(lam(X62))
| ~ nf(X62) )
& ( nf(X62)
| ~ nf(lam(X62)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_026])])]) ).
cnf(c_0_20,negated_conjecture,
~ nf(lam(lam(var(zero)))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ nf(X1)
| nf(lam(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X63] : nf(var(X63)),
inference(variable_rename,[status(thm)],[axiom_027]) ).
cnf(c_0_23,negated_conjecture,
~ nf(lam(var(zero))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
nf(var(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 10:35:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3843196 completed with status 0
% 0.11/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.43 % No SInE strategy applied
% 0.11/0.43 % Search class: FGHSM-FFMF31-SFFFFFNN
% 0.11/0.43 % partial match(1): FGHSM-FFMM31-SFFFFFNN
% 0.11/0.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.11/0.43 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.11/0.43 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.43 % SubtermCWHack with pid 3843202 completed with status 0
% 0.11/0.43 % Result found by SubtermCWHack
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.43 % No SInE strategy applied
% 0.11/0.43 % Search class: FGHSM-FFMF31-SFFFFFNN
% 0.11/0.43 % partial match(1): FGHSM-FFMM31-SFFFFFNN
% 0.11/0.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.43 % Preprocessing time : 0.001 s
% 0.11/0.43
% 0.11/0.43 % Proof found!
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
% 0.11/0.43 % Parsed axioms : 36
% 0.11/0.43 % Removed by relevancy pruning/SinE : 0
% 0.11/0.43 % Initial clauses : 43
% 0.11/0.43 % Removed in clause preprocessing : 0
% 0.11/0.43 % Initial clauses in saturation : 43
% 0.11/0.43 % Processed clauses : 62
% 0.11/0.43 % ...of these trivial : 0
% 0.11/0.43 % ...subsumed : 6
% 0.11/0.43 % ...remaining for further processing : 56
% 0.11/0.43 % Other redundant clauses eliminated : 1
% 0.11/0.43 % Clauses deleted for lack of memory : 0
% 0.11/0.43 % Backward-subsumed : 1
% 0.11/0.43 % Backward-rewritten : 0
% 0.11/0.43 % Generated clauses : 36
% 0.11/0.43 % ...of the previous two non-redundant : 26
% 0.11/0.43 % ...aggressively subsumed : 0
% 0.11/0.43 % Contextual simplify-reflections : 0
% 0.11/0.43 % Paramodulations : 33
% 0.11/0.43 % Factorizations : 0
% 0.11/0.43 % NegExts : 0
% 0.11/0.43 % Equation resolutions : 3
% 0.11/0.43 % Disequality decompositions : 0
% 0.11/0.43 % Total rewrite steps : 8
% 0.11/0.43 % ...of those cached : 1
% 0.11/0.43 % Propositional unsat checks : 0
% 0.11/0.43 % Propositional check models : 0
% 0.11/0.43 % Propositional check unsatisfiable : 0
% 0.11/0.43 % Propositional clauses : 0
% 0.11/0.43 % Propositional clauses after purity: 0
% 0.11/0.43 % Propositional unsat core size : 0
% 0.11/0.43 % Propositional preprocessing time : 0.000
% 0.11/0.43 % Propositional encoding time : 0.000
% 0.11/0.43 % Propositional solver time : 0.000
% 0.11/0.43 % Success case prop preproc time : 0.000
% 0.11/0.43 % Success case prop encoding time : 0.000
% 0.11/0.43 % Success case prop solver time : 0.000
% 0.11/0.43 % Current number of processed clauses : 54
% 0.11/0.43 % Positive orientable unit clauses : 15
% 0.11/0.43 % Positive unorientable unit clauses: 0
% 0.11/0.43 % Negative unit clauses : 15
% 0.11/0.43 % Non-unit-clauses : 24
% 0.11/0.43 % Current number of unprocessed clauses: 7
% 0.11/0.43 % ...number of literals in the above : 23
% 0.11/0.43 % Current number of archived formulas : 0
% 0.11/0.43 % Current number of archived clauses : 1
% 0.11/0.43 % Clause-clause subsumption calls (NU) : 65
% 0.11/0.43 % Rec. Clause-clause subsumption calls : 59
% 0.11/0.43 % Non-unit clause-clause subsumptions : 1
% 0.11/0.43 % Unit Clause-clause subsumption calls : 16
% 0.11/0.43 % Rewrite failures with RHS unbound : 0
% 0.11/0.43 % BW rewrite match attempts : 0
% 0.11/0.43 % BW rewrite match successes : 0
% 0.11/0.43 % Condensation attempts : 0
% 0.11/0.43 % Condensation successes : 0
% 0.11/0.43 % Termbank termtop insertions : 2566
% 0.11/0.43 % Search garbage collected termcells : 317
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.005 s
% 0.11/0.43 % System time : 0.004 s
% 0.11/0.43 % Total time : 0.009 s
% 0.11/0.43 % Maximum resident set size: 3668 pages
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.017 s
% 0.11/0.43 % System time : 0.011 s
% 0.11/0.43 % Total time : 0.028 s
% 0.11/0.43 % Maximum resident set size: 4608 pages
% 0.11/0.43 % E exiting
%------------------------------------------------------------------------------