%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG177+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 : n015.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 11:55:17 AM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 3 unt; 0 def)
% Number of atoms : 145 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 183 ( 80 ~; 60 |; 19 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 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 : 81 ( 0 sgn 34 !; 4 ?)
% 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(X1,X2) != X2 )
& 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(X1,X2) != X2 )
& 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,negated_conjecture,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( j(h(X24)) = X24
| ~ sorti1(X24) )
& ( h(j(X23)) = X23
| ~ sorti2(X23) )
& ( j(op2(X21,X22)) = op1(j(X21),j(X22))
| ~ sorti2(X22)
| ~ sorti2(X21) )
& ( h(op1(X19,X20)) = op2(h(X19),h(X20))
| ~ sorti1(X20)
| ~ sorti1(X19) )
& ( sorti1(j(X18))
| ~ sorti2(X18) )
& ( sorti2(h(X17))
| ~ sorti1(X17) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
? [X1] :
( ! [X2] :
( sorti1(X2)
=> op1(X1,X2) != X2 )
& sorti1(X1) ),
inference(fof_simplification,[status(thm)],[ax3]) ).
cnf(c_0_7,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,X2)) = op1(j(X1),j(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ sorti1(X1)
| j(h(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( ~ sorti1(X1)
| sorti2(h(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X14] :
( ( op1(esk1_0,X14) != X14
| ~ sorti1(X14) )
& 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)],[c_0_6])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| j(op2(h(X1),X2)) = op1(X1,j(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X1,X2)) = op2(h(X1),h(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( op1(esk1_0,X1) != X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti1(X1)
| op1(X1,j(h(X2))) = j(h(op1(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_9]) ).
cnf(c_0_15,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( ~ sorti2(X1)
| sorti1(j(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(j(h(X1)))
| j(h(op1(esk1_0,X1))) != j(h(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(X2)
| h(op1(X1,j(X2))) = op2(h(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| j(op2(X1,h(X2))) = op1(j(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_21,plain,
! [X11,X12] :
( sorti2(op2(X11,X12))
| ~ sorti2(X12)
| ~ sorti2(X11) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ sorti1(j(h(j(X1))))
| ~ sorti2(X1)
| j(op2(h(esk1_0),X1)) != j(h(j(X1))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op1(j(h(X1)),X2) = j(h(op1(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_9]) ).
cnf(c_0_24,plain,
( ~ sorti2(X2)
| ~ sorti2(X1)
| sorti2(op2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ sorti1(j(h(j(X1))))
| ~ sorti2(X1)
| j(h(j(X1))) != op1(esk1_0,j(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(op1(X1,X2))) = op1(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| sorti2(h(op1(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_9]),c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(op1(X1,X2))) != op1(esk1_0,op1(X1,X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| h(op1(j(X1),X2)) = op2(X1,h(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
fof(c_0_30,plain,
~ ? [X1] :
( ! [X2] :
( sorti2(X2)
=> op2(X1,X2) != X2 )
& sorti2(X1) ),
inference(fof_simplification,[status(thm)],[ax4]) ).
cnf(c_0_31,negated_conjecture,
( ~ sorti1(X2)
| ~ sorti2(X1)
| op1(esk1_0,op1(j(X1),X2)) != j(op2(X1,h(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_17]) ).
fof(c_0_32,plain,
! [X15] :
( ( ~ sorti2(X15)
| op2(X15,esk2_1(X15)) = esk2_1(X15) )
& ( ~ sorti2(X15)
| sorti2(esk2_1(X15)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X1,h(j(X2)))) != op1(esk1_0,j(op2(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_7]),c_0_17]) ).
cnf(c_0_34,plain,
( ~ sorti2(X1)
| op2(X1,esk2_1(X1)) = esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( ~ sorti2(X2)
| ~ sorti2(X1)
| op1(esk1_0,j(op2(X1,X2))) != j(op2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_36,plain,
( ~ sorti2(X1)
| sorti2(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( ~ sorti1(X1)
| ~ sorti2(esk2_1(h(X1)))
| op1(X1,j(esk2_1(h(X1)))) = j(esk2_1(h(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_34]),c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( ~ sorti2(X1)
| op1(esk1_0,j(esk2_1(X1))) != j(esk2_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ sorti1(X1)
| op1(X1,j(esk2_1(h(X1)))) = j(esk2_1(h(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_9]) ).
cnf(c_0_40,negated_conjecture,
~ sorti2(h(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_15])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_9]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG177+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:03:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1520465 completed with status 0
% 0.13/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FHHSF-FFSF21-SFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.45 % new_bool_3 with pid 1520472 completed with status 0
% 0.13/0.45 % Result found by new_bool_3
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FHHSF-FFSF21-SFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Preprocessing time : 0.001 s
% 0.13/0.45 % Presaturation interreduction done
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 5
% 0.13/0.45 % Removed by relevancy pruning/SinE : 0
% 0.13/0.45 % Initial clauses : 12
% 0.13/0.45 % Removed in clause preprocessing : 0
% 0.13/0.45 % Initial clauses in saturation : 12
% 0.13/0.45 % Processed clauses : 481
% 0.13/0.45 % ...of these trivial : 0
% 0.13/0.45 % ...subsumed : 334
% 0.13/0.45 % ...remaining for further processing : 147
% 0.13/0.45 % Other redundant clauses eliminated : 0
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 4
% 0.13/0.45 % Backward-rewritten : 0
% 0.13/0.45 % Generated clauses : 1805
% 0.13/0.45 % ...of the previous two non-redundant : 1759
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 119
% 0.13/0.45 % Paramodulations : 1805
% 0.13/0.45 % Factorizations : 0
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 0
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 16
% 0.13/0.45 % ...of those cached : 15
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 131
% 0.13/0.45 % Positive orientable unit clauses : 1
% 0.13/0.45 % Positive unorientable unit clauses: 0
% 0.13/0.45 % Negative unit clauses : 1
% 0.13/0.45 % Non-unit-clauses : 129
% 0.13/0.45 % Current number of unprocessed clauses: 1293
% 0.13/0.45 % ...number of literals in the above : 6800
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 16
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 4959
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 1786
% 0.13/0.45 % Non-unit clause-clause subsumptions : 457
% 0.13/0.45 % Unit Clause-clause subsumption calls : 20
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 0
% 0.13/0.45 % BW rewrite match successes : 0
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 33609
% 0.13/0.45 % Search garbage collected termcells : 347
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.024 s
% 0.13/0.45 % System time : 0.005 s
% 0.13/0.45 % Total time : 0.029 s
% 0.13/0.45 % Maximum resident set size: 3384 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.115 s
% 0.13/0.45 % System time : 0.021 s
% 0.13/0.45 % Total time : 0.136 s
% 0.13/0.45 % Maximum resident set size: 4608 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------