%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:50:28 AM UTC 2026
% Result : Theorem 0.14s 5.66s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 92 ( 25 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 107 ( 38 ~; 30 |; 15 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 34 !; 0 ?)
% 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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax4,axiom,
~ ~ ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> op2(X1,X2) = op2(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(ax3,axiom,
~ ! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> op1(X1,X2) = op1(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
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,
! [X23,X24] :
( op2(X23,X24) = op2(X24,X23)
| ~ sorti2(X24)
| ~ sorti2(X23) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])]) ).
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,
( ~ sorti2(X2)
| ~ sorti2(X1)
| op2(X1,X2) = op2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X1,X2)) = op2(h(X1),h(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| op2(h(X1),h(X2)) = h(op1(X2,X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_9]) ).
fof(c_0_11,plain,
! [X17,X18] :
( sorti1(op1(X17,X18))
| ~ sorti1(X18)
| ~ sorti1(X17) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ sorti1(X1)
| j(h(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X1,X2)) = h(op1(X2,X1)) ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_14,plain,
( ~ sorti1(X2)
| ~ sorti1(X1)
| sorti1(op1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| j(h(op1(X1,X2))) = op1(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
fof(c_0_16,plain,
( op1(esk1_0,esk2_0) != op1(esk2_0,esk1_0)
& sorti1(esk2_0)
& sorti1(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(op1(X1,X2))) = op1(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_18,plain,
op1(esk1_0,esk2_0) != op1(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| op1(X1,X2) = op1(X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_20,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.58 % Computer : n019.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Mon Sep 21 12:54:11 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.63 Running first-order theorem proving
% 0.14/5.63 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
% 0.14/5.66 % Version: 3.5.1
% 0.14/5.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.66 % Starting sh5l with 300s (1) cores
% 0.14/5.66 % new_bool_3 with pid 2619982 completed with status 0
% 0.14/5.66 % Result found by new_bool_3
% 0.14/5.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.66 % Search class: FHUSF-FFSF21-SFFFFFNN
% 0.14/5.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.66 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.66 % SubtermCWHack with pid 2619988 completed with status 0
% 0.14/5.66 % Result found by SubtermCWHack
% 0.14/5.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.66 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.66 % Search class: FHUSF-FFSF21-SFFFFFNN
% 0.14/5.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.66 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.66 % Preprocessing time : 0.001 s
% 0.14/5.66
% 0.14/5.66 % Proof found!
% 0.14/5.66 % SZS status Theorem
% 0.14/5.66 % SZS output start CNFRefutation
% See solution above
% 0.14/5.66 % Parsed axioms : 5
% 0.14/5.66 % Removed by relevancy pruning/SinE : 0
% 0.14/5.66 % Initial clauses : 12
% 0.14/5.66 % Removed in clause preprocessing : 0
% 0.14/5.66 % Initial clauses in saturation : 12
% 0.14/5.66 % Processed clauses : 139
% 0.14/5.66 % ...of these trivial : 0
% 0.14/5.66 % ...subsumed : 100
% 0.14/5.66 % ...remaining for further processing : 39
% 0.14/5.66 % Other redundant clauses eliminated : 0
% 0.14/5.66 % Clauses deleted for lack of memory : 0
% 0.14/5.66 % Backward-subsumed : 0
% 0.14/5.66 % Backward-rewritten : 0
% 0.14/5.66 % Generated clauses : 372
% 0.14/5.66 % ...of the previous two non-redundant : 333
% 0.14/5.66 % ...aggressively subsumed : 0
% 0.14/5.66 % Contextual simplify-reflections : 27
% 0.14/5.66 % Paramodulations : 372
% 0.14/5.66 % Factorizations : 0
% 0.14/5.66 % NegExts : 0
% 0.14/5.66 % Equation resolutions : 0
% 0.14/5.66 % Disequality decompositions : 0
% 0.14/5.66 % Total rewrite steps : 2
% 0.14/5.66 % ...of those cached : 0
% 0.14/5.66 % Propositional unsat checks : 0
% 0.14/5.66 % Propositional check models : 0
% 0.14/5.66 % Propositional check unsatisfiable : 0
% 0.14/5.66 % Propositional clauses : 0
% 0.14/5.66 % Propositional clauses after purity: 0
% 0.14/5.66 % Propositional unsat core size : 0
% 0.14/5.66 % Propositional preprocessing time : 0.000
% 0.14/5.66 % Propositional encoding time : 0.000
% 0.14/5.66 % Propositional solver time : 0.000
% 0.14/5.66 % Success case prop preproc time : 0.000
% 0.14/5.66 % Success case prop encoding time : 0.000
% 0.14/5.66 % Success case prop solver time : 0.000
% 0.14/5.66 % Current number of processed clauses : 39
% 0.14/5.66 % Positive orientable unit clauses : 2
% 0.14/5.66 % Positive unorientable unit clauses: 0
% 0.14/5.66 % Negative unit clauses : 1
% 0.14/5.66 % Non-unit-clauses : 36
% 0.14/5.66 % Current number of unprocessed clauses: 206
% 0.14/5.66 % ...number of literals in the above : 965
% 0.14/5.66 % Current number of archived formulas : 0
% 0.14/5.66 % Current number of archived clauses : 0
% 0.14/5.66 % Clause-clause subsumption calls (NU) : 633
% 0.14/5.66 % Rec. Clause-clause subsumption calls : 421
% 0.14/5.66 % Non-unit clause-clause subsumptions : 127
% 0.14/5.66 % Unit Clause-clause subsumption calls : 0
% 0.14/5.66 % Rewrite failures with RHS unbound : 0
% 0.14/5.66 % BW rewrite match attempts : 0
% 0.14/5.66 % BW rewrite match successes : 0
% 0.14/5.66 % Condensation attempts : 0
% 0.14/5.66 % Condensation successes : 0
% 0.14/5.66 % Termbank termtop insertions : 6398
% 0.14/5.66 % Search garbage collected termcells : 331
% 0.14/5.66
% 0.14/5.66 % -------------------------------------------------
% 0.14/5.66 % User time : 0.007 s
% 0.14/5.66 % System time : 0.002 s
% 0.14/5.66 % Total time : 0.009 s
% 0.14/5.66 % Maximum resident set size: 3640 pages
% 0.14/5.66
% 0.14/5.66 % -------------------------------------------------
% 0.14/5.66 % User time : 0.009 s
% 0.14/5.66 % System time : 0.007 s
% 0.14/5.66 % Total time : 0.015 s
% 0.14/5.66 % Maximum resident set size: 4864 pages
% 0.14/5.66 % E exiting
%------------------------------------------------------------------------------