%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM691^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Wed Sep 30 08:16:51 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 28 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 294 ( 40 ~; 24 |; 3 &; 208 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
z: nat ).
thf(decl_26,type,
u: nat ).
thf(decl_27,type,
more: nat > nat > $o ).
thf(decl_28,type,
pl: nat > nat > nat ).
thf(satz23,conjecture,
( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p',satz23) ).
thf(satz22b,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ X2 @ X3 )
=> ( ( ~ ( more @ X4 @ X5 )
=> ( X4 = X5 ) )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p',satz22b) ).
thf(n,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p',n) ).
thf(m,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p',m) ).
thf(satz22a,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( ~ ( more @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( ( more @ X4 @ X5 )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p',satz22a) ).
thf(c_0_5,negated_conjecture,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(assume_negation,[status(cth)],[satz23]) ).
thf(c_0_6,negated_conjecture,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ X2 @ X3 )
=> ( ( ~ ( more @ X4 @ X5 )
=> ( X4 = X5 ) )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz22b]) ).
thf(c_0_8,negated_conjecture,
( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
& ( ( pl @ x @ z )
!= ( pl @ y @ u ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
thf(c_0_9,plain,
! [X18: nat,X19: nat,X20: nat,X21: nat] :
( ( ~ ( more @ X20 @ X21 )
| ( more @ ( pl @ X18 @ X20 ) @ ( pl @ X19 @ X21 ) )
| ~ ( more @ X18 @ X19 ) )
& ( ( X20 != X21 )
| ( more @ ( pl @ X18 @ X20 ) @ ( pl @ X19 @ X21 ) )
| ~ ( more @ X18 @ X19 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_10,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(fof_simplification,[status(thm)],[n]) ).
thf(c_0_11,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ ( pl @ X4 @ X2 ) @ ( pl @ X5 @ X3 ) )
| ~ ( more @ X2 @ X3 )
| ~ ( more @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( ( more @ z @ u )
| ( z = u ) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_15,negated_conjecture,
( ~ ( more @ x @ y )
| ~ ( more @ z @ u ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
( ( more @ z @ u )
| ( z = u ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( z = u )
| ~ ( more @ x @ y ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
( ( y = x )
| ( z = u ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_21,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ ( pl @ X4 @ X2 ) @ ( pl @ X5 @ X3 ) )
| ( X2 != X3 )
| ~ ( more @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_22,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( ~ ( more @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( ( more @ X4 @ X5 )
=> ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz22a]) ).
thf(c_0_23,negated_conjecture,
( ( y = x )
| ~ ( more @ ( pl @ x @ u ) @ ( pl @ y @ u ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
thf(c_0_24,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X4 @ X3 ) )
| ~ ( more @ X2 @ X4 ) ),
inference(er,[status(thm)],[c_0_21]) ).
thf(c_0_25,plain,
! [X14: nat,X15: nat,X16: nat,X17: nat] :
( ( ~ ( more @ X14 @ X15 )
| ~ ( more @ X16 @ X17 )
| ( more @ ( pl @ X14 @ X16 ) @ ( pl @ X15 @ X17 ) ) )
& ( ( X14 != X15 )
| ~ ( more @ X16 @ X17 )
| ( more @ ( pl @ X14 @ X16 ) @ ( pl @ X15 @ X17 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
thf(c_0_26,negated_conjecture,
y = x,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]) ).
thf(c_0_27,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( more @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) )
| ( X2 != X3 )
| ~ ( more @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) ),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
thf(c_0_29,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( more @ ( pl @ X2 @ X3 ) @ ( pl @ X2 @ X4 ) )
| ~ ( more @ X3 @ X4 ) ),
inference(er,[status(thm)],[c_0_27]) ).
thf(c_0_30,negated_conjecture,
( ( pl @ x @ z )
!= ( pl @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_31,negated_conjecture,
~ ( more @ z @ u ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,negated_conjecture,
( ( pl @ x @ z )
!= ( pl @ x @ u ) ),
inference(rw,[status(thm)],[c_0_30,c_0_26]) ).
thf(c_0_33,plain,
z = u,
inference(sr,[status(thm)],[c_0_16,c_0_31]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM691^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:39:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.pyfp61gf3r/E---3.1_45610.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.14 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.14 % Starting new_ho_10_unif with 300s (1) cores
% 0.08/0.14 % new_bool_1 with pid 45624 completed with status 0
% 0.08/0.14 % Result found by new_bool_1
% 0.08/0.14 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.14 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.14 % Search class: HGUSF-FFSF22-SFFFFFNN
% 0.08/0.14 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.14 % SubtermCWHack with pid 45628 completed with status 0
% 0.08/0.14 % Result found by SubtermCWHack
% 0.08/0.14 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.15 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.15 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.15 % Search class: HGUSF-FFSF22-SFFFFFNN
% 0.08/0.15 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 13
% 0.08/0.15 % Removed by relevancy pruning/SinE : 8
% 0.08/0.15 % Initial clauses : 8
% 0.08/0.15 % Removed in clause preprocessing : 0
% 0.08/0.15 % Initial clauses in saturation : 8
% 0.08/0.15 % Processed clauses : 23
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 2
% 0.08/0.15 % ...remaining for further processing : 21
% 0.08/0.15 % Other redundant clauses eliminated : 2
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 1
% 0.08/0.15 % Backward-rewritten : 10
% 0.08/0.15 % Generated clauses : 16
% 0.08/0.15 % ...of the previous two non-redundant : 17
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 2
% 0.08/0.15 % Paramodulations : 13
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 2
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 10
% 0.08/0.15 % ...of those cached : 8
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 7
% 0.08/0.15 % Positive orientable unit clauses : 2
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 2
% 0.08/0.15 % Non-unit-clauses : 3
% 0.08/0.15 % Current number of unprocessed clauses: 1
% 0.08/0.15 % ...number of literals in the above : 2
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 12
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 19
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 19
% 0.08/0.15 % Non-unit clause-clause subsumptions : 4
% 0.08/0.15 % Unit Clause-clause subsumption calls : 3
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 2
% 0.08/0.15 % BW rewrite match successes : 2
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 830
% 0.08/0.15 % Search garbage collected termcells : 127
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.004 s
% 0.08/0.15 % System time : 0.000 s
% 0.08/0.15 % Total time : 0.004 s
% 0.08/0.15 % Maximum resident set size: 3636 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.004 s
% 0.08/0.15 % System time : 0.003 s
% 0.08/0.15 % Total time : 0.007 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------