%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:16:42 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 73 equ; 0 cnn)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 232 ( 56 ~; 26 |; 7 &; 128 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
pl: nat > nat > nat ).
thf(decl_26,type,
esk1_0: nat ).
thf(decl_27,type,
esk2_0: nat ).
thf(decl_28,type,
esk3_0: nat ).
thf(decl_29,type,
esk4_0: nat ).
thf(satz7,axiom,
! [X1: nat,X2: nat] :
( X2
!= ( pl @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.gxIOYF04i5/E---3.1_3288996.p',satz7) ).
thf(satz9b,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) ) )
=> ~ ~ ( ( ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) )
=> ~ ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) ) )
=> ~ ( ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gxIOYF04i5/E---3.1_3288996.p',satz9b) ).
thf(satz5,axiom,
! [X1: nat,X2: nat,X4: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X4 )
= ( pl @ X1 @ ( pl @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gxIOYF04i5/E---3.1_3288996.p',satz5) ).
thf(satz6,axiom,
! [X1: nat,X2: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.gxIOYF04i5/E---3.1_3288996.p',satz6) ).
thf(c_0_4,plain,
! [X1: nat,X2: nat] :
( X2
!= ( pl @ X1 @ X2 ) ),
inference(fof_simplification,[status(thm)],[satz7]) ).
thf(c_0_5,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) ) )
=> ~ ~ ( ( ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) )
=> ~ ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) ) )
=> ~ ( ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) )
=> ( x != y ) ) ) ),
inference(assume_negation,[status(cth)],[satz9b]) ).
thf(c_0_6,plain,
! [X18: nat,X19: nat] :
( X19
!= ( pl @ X18 @ X19 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_4])]) ).
thf(c_0_7,plain,
! [X22: nat,X23: nat,X24: nat] :
( ( pl @ ( pl @ X22 @ X23 ) @ X24 )
= ( pl @ X22 @ ( pl @ X23 @ X24 ) ) ),
inference(variable_rename,[status(thm)],[satz5]) ).
thf(c_0_8,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) ) )
=> ~ ~ ( ( ~ ! [X5: nat] :
( x
!= ( pl @ y @ X5 ) )
=> ~ ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) ) )
=> ~ ( ~ ! [X5: nat] :
( y
!= ( pl @ x @ X5 ) )
=> ( x != y ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X2: nat,X1: nat] :
( X1
!= ( pl @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: nat,X2: nat,X4: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X4 )
= ( pl @ X1 @ ( pl @ X2 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X20: nat,X21: nat] :
( ( pl @ X20 @ X21 )
= ( pl @ X21 @ X20 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_12,negated_conjecture,
( ( ( y
= ( pl @ x @ esk4_0 ) )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x = y ) )
& ( ( x = y )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x = y ) )
& ( ( y
= ( pl @ x @ esk4_0 ) )
| ( y
= ( pl @ x @ esk3_0 ) )
| ( x = y ) )
& ( ( x = y )
| ( y
= ( pl @ x @ esk3_0 ) )
| ( x = y ) )
& ( ( y
= ( pl @ x @ esk4_0 ) )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x
= ( pl @ y @ esk1_0 ) ) )
& ( ( x = y )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x
= ( pl @ y @ esk1_0 ) ) )
& ( ( y
= ( pl @ x @ esk4_0 ) )
| ( y
= ( pl @ x @ esk3_0 ) )
| ( x
= ( pl @ y @ esk1_0 ) ) )
& ( ( x = y )
| ( y
= ( pl @ x @ esk3_0 ) )
| ( x
= ( pl @ y @ esk1_0 ) ) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_13,plain,
! [X1: nat,X2: nat,X4: nat] :
( ( pl @ X1 @ ( pl @ X2 @ X4 ) )
!= X4 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X2: nat,X1: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( x = y )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X1: nat,X4: nat,X2: nat] :
( ( pl @ X1 @ ( pl @ X2 @ X4 ) )
!= X2 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( y = x )
| ( x
= ( pl @ y @ esk2_0 ) ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: nat] :
( ( x = y )
| ( ( pl @ X1 @ x )
!= y ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
( ( x = y )
| ( y
= ( pl @ x @ esk3_0 ) )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,negated_conjecture,
! [X1: nat] :
( ( x = y )
| ( ( pl @ x @ X1 )
!= y ) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
thf(c_0_21,negated_conjecture,
( ( y = x )
| ( y
= ( pl @ x @ esk3_0 ) ) ),
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
( ( y
= ( pl @ x @ esk4_0 ) )
| ( x
= ( pl @ y @ esk2_0 ) )
| ( x
= ( pl @ y @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_23,negated_conjecture,
x = y,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,plain,
! [X2: nat,X1: nat] :
( ( pl @ X1 @ X2 )
!= X1 ),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_24]),c_0_24]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM651^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n007.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:29:40 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.gxIOYF04i5/E---3.1_3288996.p
% 0.08/0.24 % Version: 3.5.1-ho
% 0.08/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.24 % Starting sh4l with 300s (1) cores
% 0.08/0.24 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.24 % ho_unfolding_6 with pid 3289010 completed with status 0
% 0.08/0.24 % Result found by ho_unfolding_6
% 0.08/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUPS-FFSM22-SFFFFFNN
% 0.08/0.24 % partial match(2): HUUPS-FFSF22-SFFFFFNN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % SubtermCWHack with pid 3289013 completed with status 0
% 0.08/0.24 % Result found by SubtermCWHack
% 0.08/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGUPS-FFSM22-SFFFFFNN
% 0.08/0.24 % partial match(2): HUUPS-FFSF22-SFFFFFNN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % Preprocessing time : 0.001 s
% 0.08/0.24
% 0.08/0.24 % Proof found!
% 0.08/0.24 % SZS status Theorem
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24 % Parsed axioms : 9
% 0.08/0.24 % Removed by relevancy pruning/SinE : 0
% 0.08/0.24 % Initial clauses : 16
% 0.08/0.24 % Removed in clause preprocessing : 5
% 0.08/0.24 % Initial clauses in saturation : 11
% 0.08/0.24 % Processed clauses : 55
% 0.08/0.24 % ...of these trivial : 1
% 0.08/0.24 % ...subsumed : 28
% 0.08/0.24 % ...remaining for further processing : 25
% 0.08/0.24 % Other redundant clauses eliminated : 0
% 0.08/0.24 % Clauses deleted for lack of memory : 0
% 0.08/0.24 % Backward-subsumed : 0
% 0.08/0.24 % Backward-rewritten : 13
% 0.08/0.24 % Generated clauses : 90
% 0.08/0.24 % ...of the previous two non-redundant : 87
% 0.08/0.24 % ...aggressively subsumed : 0
% 0.08/0.24 % Contextual simplify-reflections : 0
% 0.08/0.24 % Paramodulations : 90
% 0.08/0.24 % Factorizations : 0
% 0.08/0.24 % NegExts : 0
% 0.08/0.24 % Equation resolutions : 0
% 0.08/0.24 % Disequality decompositions : 0
% 0.08/0.24 % Total rewrite steps : 57
% 0.08/0.24 % ...of those cached : 46
% 0.08/0.24 % Propositional unsat checks : 0
% 0.08/0.24 % Propositional check models : 0
% 0.08/0.24 % Propositional check unsatisfiable : 0
% 0.08/0.24 % Propositional clauses : 0
% 0.08/0.24 % Propositional clauses after purity: 0
% 0.08/0.24 % Propositional unsat core size : 0
% 0.08/0.24 % Propositional preprocessing time : 0.000
% 0.08/0.24 % Propositional encoding time : 0.000
% 0.08/0.24 % Propositional solver time : 0.000
% 0.08/0.24 % Success case prop preproc time : 0.000
% 0.08/0.24 % Success case prop encoding time : 0.000
% 0.08/0.24 % Success case prop solver time : 0.000
% 0.08/0.24 % Current number of processed clauses : 12
% 0.08/0.24 % Positive orientable unit clauses : 2
% 0.08/0.24 % Positive unorientable unit clauses: 1
% 0.08/0.24 % Negative unit clauses : 9
% 0.08/0.24 % Non-unit-clauses : 0
% 0.08/0.24 % Current number of unprocessed clauses: 34
% 0.08/0.24 % ...number of literals in the above : 42
% 0.08/0.24 % Current number of archived formulas : 0
% 0.08/0.24 % Current number of archived clauses : 13
% 0.08/0.24 % Clause-clause subsumption calls (NU) : 96
% 0.08/0.24 % Rec. Clause-clause subsumption calls : 96
% 0.08/0.24 % Non-unit clause-clause subsumptions : 5
% 0.08/0.24 % Unit Clause-clause subsumption calls : 12
% 0.08/0.24 % Rewrite failures with RHS unbound : 0
% 0.08/0.24 % BW rewrite match attempts : 3
% 0.08/0.24 % BW rewrite match successes : 3
% 0.08/0.24 % Condensation attempts : 0
% 0.08/0.24 % Condensation successes : 0
% 0.08/0.24 % Termbank termtop insertions : 1231
% 0.08/0.24 % Search garbage collected termcells : 152
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.003 s
% 0.08/0.24 % System time : 0.002 s
% 0.08/0.24 % Total time : 0.006 s
% 0.08/0.24 % Maximum resident set size: 3892 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.004 s
% 0.08/0.24 % System time : 0.007 s
% 0.08/0.24 % Total time : 0.011 s
% 0.08/0.24 % Maximum resident set size: 4864 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------