%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:50:30 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 94 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 104 ( 36 ~; 29 |; 17 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 2 sgn 32 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax3,axiom,
? [X1] :
( ! [X2] :
( sorti1(X2)
=> op1(X2,X2) = X1 )
& sorti1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(ax4,axiom,
~ ? [X1] :
( ! [X2] :
( sorti2(X2)
=> op2(X2,X2) = X1 )
& sorti2(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,plain,
! [X20] :
( ( op1(X20,X20) = esk1_0
| ~ sorti1(X20) )
& sorti1(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)],[ax3])])])])]) ).
fof(c_0_6,negated_conjecture,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( j(h(X16)) = X16
| ~ sorti1(X16) )
& ( h(j(X15)) = X15
| ~ sorti2(X15) )
& ( j(op2(X13,X14)) = op1(j(X13),j(X14))
| ~ sorti2(X14)
| ~ sorti2(X13) )
& ( h(op1(X11,X12)) = op2(h(X11),h(X12))
| ~ sorti1(X12)
| ~ sorti1(X11) )
& ( sorti1(j(X10))
| ~ sorti2(X10) )
& ( sorti2(h(X9))
| ~ sorti1(X9) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( ~ sorti1(X1)
| op1(X1,X1) = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,X2)) = op1(j(X1),j(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ sorti2(X1)
| sorti1(j(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( ~ sorti2(X1)
| j(op2(X1,X1)) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_12,plain,
! [X21,X22] :
( sorti2(op2(X21,X22))
| ~ sorti2(X22)
| ~ sorti2(X21) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ sorti2(X1)
| ~ sorti2(op2(X1,X1))
| op2(X1,X1) = h(esk1_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ sorti2(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( ~ sorti2(X1)
| op2(X1,X1) = h(esk1_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
( ~ sorti2(X1)
| sorti2(h(esk1_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_18,plain,
! [X23] :
( ( ~ sorti2(X23)
| op2(esk2_1(X23),esk2_1(X23)) != X23 )
& ( ~ sorti2(X23)
| sorti2(esk2_1(X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(esk1_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,plain,
( ~ sorti2(X1)
| op2(esk2_1(X1),esk2_1(X1)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
sorti2(h(esk1_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ sorti2(esk2_1(h(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15])]),c_0_22])]) ).
cnf(c_0_24,plain,
( ~ sorti2(X1)
| sorti2(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.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 12:59:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_3 with pid 3170674 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FHHSF-FFSF21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 3170684 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FHHSF-FFSF21-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 5
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 12
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 12
% 0.11/0.45 % Processed clauses : 23
% 0.11/0.45 % ...of these trivial : 0
% 0.11/0.45 % ...subsumed : 1
% 0.11/0.45 % ...remaining for further processing : 22
% 0.11/0.45 % Other redundant clauses eliminated : 1
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 1
% 0.11/0.45 % Backward-rewritten : 3
% 0.11/0.45 % Generated clauses : 38
% 0.11/0.45 % ...of the previous two non-redundant : 30
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 3
% 0.11/0.45 % Paramodulations : 37
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 1
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 12
% 0.11/0.45 % ...of those cached : 9
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 18
% 0.11/0.45 % Positive orientable unit clauses : 3
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 1
% 0.11/0.45 % Non-unit-clauses : 14
% 0.11/0.45 % Current number of unprocessed clauses: 18
% 0.11/0.45 % ...number of literals in the above : 61
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 4
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 10
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 10
% 0.11/0.45 % Non-unit clause-clause subsumptions : 5
% 0.11/0.45 % Unit Clause-clause subsumption calls : 1
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 2
% 0.11/0.45 % BW rewrite match successes : 2
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 1548
% 0.11/0.45 % Search garbage collected termcells : 332
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.003 s
% 0.11/0.45 % System time : 0.004 s
% 0.11/0.45 % Total time : 0.007 s
% 0.11/0.45 % Maximum resident set size: 3640 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.005 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.013 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------