%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:11:38 PM UTC 2026
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 129 ( 49 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 152 ( 56 ~; 49 |; 30 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 156 ( 7 sgn 107 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('T-subst-abs-3',axiom,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-3') ).
fof('T-subst-abs-2',axiom,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& ~ visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2') ).
fof('T-subst-abs',conjecture,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs') ).
fof('T-Strong',axiom,
! [X9,X10,X20,X11,X15] :
( ( vtcheck(vbind(X9,X10,X20),X11,X15)
& ~ visFreeVar(X9,X11) )
=> vtcheck(X20,X11,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
fof(isFreeVar1,axiom,
! [X15,X1,X4,X9,X14,X11] :
( ( X4 = vabs(X9,X15,X11)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X11)
& X9 != X14 ) )
& ( ( visFreeVar(X14,X11)
& X9 != X14 )
=> visFreeVar(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).
fof(subst3,axiom,
! [X11,X9,X1,X4,X6,X19,X21,X15,X12] :
( ( X6 = vabs(X21,X15,X12)
& X4 = X11
& X1 = X9 )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vabs(X21,X15,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst3) ).
fof(c_0_6,plain,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(fof_simplification,[status(thm)],['T-subst-abs-3']) ).
fof(c_0_7,plain,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& ~ visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(fof_simplification,[status(thm)],['T-subst-abs-2']) ).
fof(c_0_8,plain,
! [X137,X138,X139,X140,X141,X142,X143] :
( vtcheck(X138,vsubst(X139,X140,vabs(X141,X142,veabs)),X143)
| ~ vtcheck(vbind(X139,X137,X138),vabs(X141,X142,veabs),X143)
| ~ vtcheck(X138,X140,X137)
| ~ visFreeVar(X141,X140)
| X139 = X141 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X130,X131,X132,X133,X134,X135,X136] :
( vtcheck(X131,vsubst(X132,X133,vabs(X134,X135,veabs)),X136)
| ~ vtcheck(vbind(X132,X130,X131),vabs(X134,X135,veabs),X136)
| ~ vtcheck(X131,X133,X130)
| visFreeVar(X134,X133)
| X132 = X134 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(assume_negation,[status(cth)],['T-subst-abs']) ).
cnf(c_0_11,plain,
( ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7)
| ~ vtcheck(X4,X3,X5)
| ~ visFreeVar(X2,X3)
| vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7)
| ~ vtcheck(X4,X3,X5)
| vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
| visFreeVar(X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
( ~ vtcheck(esk2_0,vsubst(esk3_0,esk4_0,vabs(esk5_0,esk6_0,veabs)),esk7_0)
& vtcheck(vbind(esk3_0,esk1_0,esk2_0),vabs(esk5_0,esk6_0,veabs),esk7_0)
& vtcheck(esk2_0,esk4_0,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_14,plain,
! [X9,X10,X20,X11,X15] :
( ( vtcheck(vbind(X9,X10,X20),X11,X15)
& ~ visFreeVar(X9,X11) )
=> vtcheck(X20,X11,X15) ),
inference(fof_simplification,[status(thm)],['T-Strong']) ).
fof(c_0_15,plain,
! [X15,X1,X4,X9,X14,X11] :
( ( X4 = vabs(X9,X15,X11)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X11)
& X9 != X14 ) )
& ( ( visFreeVar(X14,X11)
& X9 != X14 )
=> visFreeVar(X1,X4) ) ) ),
inference(fof_simplification,[status(thm)],[isFreeVar1]) ).
cnf(c_0_16,plain,
( ~ vtcheck(X3,X4,X7)
| ~ vtcheck(vbind(X1,X7,X3),vabs(X2,X5,veabs),X6)
| vtcheck(X3,vsubst(X1,X4,vabs(X2,X5,veabs)),X6)
| X1 = X2 ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
vtcheck(vbind(esk3_0,esk1_0,esk2_0),vabs(esk5_0,esk6_0,veabs),esk7_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X96,X97,X98,X99,X100,X101,X102,X103,X104] :
( X101 = vabs(X102,X103,X104)
| X101 != vsubst(X98,X99,X100)
| X97 != X102
| X100 != vabs(X102,X103,X104)
| X99 != X96
| X98 != X97 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst3])])]) ).
fof(c_0_19,plain,
! [X56,X57,X58,X59,X60] :
( vtcheck(X58,X59,X60)
| ~ vtcheck(vbind(X56,X57,X58),X59,X60)
| visFreeVar(X56,X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_20,plain,
! [X154,X155,X156,X157,X158,X159] :
( ( X156 != vabs(X157,X154,X159)
| X155 != X158
| ~ visFreeVar(X155,X156)
| visFreeVar(X158,X159) )
& ( X156 != vabs(X157,X154,X159)
| X155 != X158
| ~ visFreeVar(X155,X156)
| X157 != X158 )
& ( X156 != vabs(X157,X154,X159)
| X155 != X158
| visFreeVar(X155,X156)
| ~ visFreeVar(X158,X159)
| X157 = X158 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_21,negated_conjecture,
~ vtcheck(esk2_0,vsubst(esk3_0,esk4_0,vabs(esk5_0,esk6_0,veabs)),esk7_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( ~ vtcheck(esk2_0,X1,esk1_0)
| vtcheck(esk2_0,vsubst(esk3_0,X1,vabs(esk5_0,esk6_0,veabs)),esk7_0)
| esk5_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
vtcheck(esk2_0,esk4_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( X9 != vsubst(X1,X3,X5)
| X2 != X6
| X5 != vabs(X6,X7,X8)
| X3 != X4
| X1 != X2
| X9 = vabs(X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ vtcheck(vbind(X1,X3,X4),X2,X5)
| vtcheck(X4,X2,X5)
| visFreeVar(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( X4 != vabs(X1,X5,X6)
| X3 != X2
| ~ visFreeVar(X3,X4)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
esk5_0 = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_28,plain,
vsubst(X1,X2,vabs(X1,X3,X4)) = vabs(X1,X3,X4),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])])])])]) ).
cnf(c_0_29,negated_conjecture,
( visFreeVar(esk3_0,vabs(esk5_0,esk6_0,veabs))
| vtcheck(esk2_0,vabs(esk5_0,esk6_0,veabs),esk7_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_30,plain,
~ visFreeVar(X1,vabs(X1,X2,X3)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])])]) ).
cnf(c_0_31,negated_conjecture,
~ vtcheck(esk2_0,vabs(esk3_0,esk6_0,veabs),esk7_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM133+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:18:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.50 % Version: 3.5.1
% 0.14/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.50 % Starting sh5l with 300s (1) cores
% 0.14/0.50 % new_bool_3 with pid 1202495 completed with status 0
% 0.14/0.50 % Result found by new_bool_3
% 0.14/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.50 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.14/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.50 % SubtermCWHack with pid 1202499 completed with status 0
% 0.14/0.50 % Result found by SubtermCWHack
% 0.14/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.50 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.14/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.50 % Preprocessing time : 0.002 s
% 0.14/0.50
% 0.14/0.50 % Proof found!
% 0.14/0.50 % SZS status Theorem
% 0.14/0.50 % SZS output start CNFRefutation
% See solution above
% 0.14/0.50 % Parsed axioms : 62
% 0.14/0.50 % Removed by relevancy pruning/SinE : 38
% 0.14/0.50 % Initial clauses : 40
% 0.14/0.50 % Removed in clause preprocessing : 4
% 0.14/0.50 % Initial clauses in saturation : 36
% 0.14/0.50 % Processed clauses : 364
% 0.14/0.50 % ...of these trivial : 0
% 0.14/0.50 % ...subsumed : 244
% 0.14/0.50 % ...remaining for further processing : 119
% 0.14/0.50 % Other redundant clauses eliminated : 127
% 0.14/0.50 % Clauses deleted for lack of memory : 0
% 0.14/0.50 % Backward-subsumed : 1
% 0.14/0.50 % Backward-rewritten : 1
% 0.14/0.50 % Generated clauses : 1327
% 0.14/0.50 % ...of the previous two non-redundant : 1212
% 0.14/0.50 % ...aggressively subsumed : 0
% 0.14/0.50 % Contextual simplify-reflections : 1
% 0.14/0.50 % Paramodulations : 1217
% 0.14/0.50 % Factorizations : 1
% 0.14/0.50 % NegExts : 0
% 0.14/0.50 % Equation resolutions : 136
% 0.14/0.50 % Disequality decompositions : 0
% 0.14/0.50 % Total rewrite steps : 164
% 0.14/0.50 % ...of those cached : 146
% 0.14/0.50 % Propositional unsat checks : 0
% 0.14/0.50 % Propositional check models : 0
% 0.14/0.50 % Propositional check unsatisfiable : 0
% 0.14/0.50 % Propositional clauses : 0
% 0.14/0.50 % Propositional clauses after purity: 0
% 0.14/0.50 % Propositional unsat core size : 0
% 0.14/0.50 % Propositional preprocessing time : 0.000
% 0.14/0.50 % Propositional encoding time : 0.000
% 0.14/0.50 % Propositional solver time : 0.000
% 0.14/0.50 % Success case prop preproc time : 0.000
% 0.14/0.50 % Success case prop encoding time : 0.000
% 0.14/0.50 % Success case prop solver time : 0.000
% 0.14/0.50 % Current number of processed clauses : 102
% 0.14/0.50 % Positive orientable unit clauses : 9
% 0.14/0.50 % Positive unorientable unit clauses: 7
% 0.14/0.50 % Negative unit clauses : 11
% 0.14/0.50 % Non-unit-clauses : 75
% 0.14/0.50 % Current number of unprocessed clauses: 884
% 0.14/0.50 % ...number of literals in the above : 4838
% 0.14/0.50 % Current number of archived formulas : 0
% 0.14/0.50 % Current number of archived clauses : 2
% 0.14/0.50 % Clause-clause subsumption calls (NU) : 2181
% 0.14/0.50 % Rec. Clause-clause subsumption calls : 1198
% 0.14/0.50 % Non-unit clause-clause subsumptions : 144
% 0.14/0.50 % Unit Clause-clause subsumption calls : 87
% 0.14/0.50 % Rewrite failures with RHS unbound : 139
% 0.14/0.50 % BW rewrite match attempts : 437
% 0.14/0.50 % BW rewrite match successes : 12
% 0.14/0.50 % Condensation attempts : 0
% 0.14/0.50 % Condensation successes : 0
% 0.14/0.50 % Termbank termtop insertions : 24010
% 0.14/0.50 % Search garbage collected termcells : 1355
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.039 s
% 0.14/0.50 % System time : 0.004 s
% 0.14/0.50 % Total time : 0.043 s
% 0.14/0.50 % Maximum resident set size: 3704 pages
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.043 s
% 0.14/0.50 % System time : 0.009 s
% 0.14/0.50 % Total time : 0.052 s
% 0.14/0.50 % Maximum resident set size: 4864 pages
% 0.14/0.50 % E exiting
%------------------------------------------------------------------------------