%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG287^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 07:44:51 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 129 ( 12 ~; 4 |; 22 &; 82 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
v: a ).
thf(decl_24,type,
u: a ).
thf(decl_25,type,
y: a ).
thf(decl_26,type,
x: a ).
thf(decl_27,type,
cP: a > a > a ).
thf(decl_28,type,
cR: a > a ).
thf(decl_29,type,
cL: a > a ).
thf(decl_30,type,
cZ: a ).
thf(cPU_P_INJ_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( x = y )
& ( u = v ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FcNX4ynYlq/E---3.1_675289.p',cPU_P_INJ_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( x = y )
& ( u = v ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_P_INJ_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( x = y )
& ( u = v ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X9: a,X10: a,X11: a,X12: a,X13: a] :
( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ ( cP @ X9 @ X10 ) )
= X9 )
& ( ( cR @ ( cP @ X11 @ X12 ) )
= X12 )
& ( ( X13 = cZ )
| ( X13
= ( cP @ ( cL @ X13 ) @ ( cR @ X13 ) ) ) )
& ( ( X13
!= ( cP @ ( cL @ X13 ) @ ( cR @ X13 ) ) )
| ( X13 != cZ ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( ( x != y )
| ( u != v ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
thf(c_0_4,negated_conjecture,
! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( cP @ x @ u )
= ( cP @ y @ v ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
v = u,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_4]) ).
thf(c_0_7,negated_conjecture,
( ( x != y )
| ( u != v ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X2: a,X1: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
( ( cP @ y @ u )
= ( cP @ x @ u ) ),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
y != x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_6])]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG287^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n016.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 17:42:34 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.FcNX4ynYlq/E---3.1_675289.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % Starting sh4l with 300s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.25 % ho_unfolding_6 with pid 675316 completed with status 0
% 0.08/0.25 % Result found by ho_unfolding_6
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGHPS-FFSS21-SFFFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 675319 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGHPS-FFSS21-SFFFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 10
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 17
% 0.08/0.25 % Removed in clause preprocessing : 9
% 0.08/0.25 % Initial clauses in saturation : 8
% 0.08/0.25 % Processed clauses : 9
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 9
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 2
% 0.08/0.25 % Generated clauses : 4
% 0.08/0.25 % ...of the previous two non-redundant : 4
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 4
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 6
% 0.08/0.25 % ...of those cached : 3
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 7
% 0.08/0.25 % Positive orientable unit clauses : 6
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 0
% 0.08/0.25 % Current number of unprocessed clauses: 2
% 0.08/0.25 % ...number of literals in the above : 4
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 2
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 1
% 0.08/0.25 % BW rewrite match successes : 1
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 641
% 0.08/0.25 % Search garbage collected termcells : 158
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.004 s
% 0.08/0.25 % Maximum resident set size: 3632 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.007 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4608 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------