%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM759^1 : 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 : n018.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 08:17:02 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 159 ( 15 ~; 11 |; 0 &; 130 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
frac: $tType ).
thf(decl_23,type,
x: frac ).
thf(decl_24,type,
y: frac ).
thf(decl_25,type,
z: frac ).
thf(decl_26,type,
eq: frac > frac > $o ).
thf(decl_27,type,
pf: frac > frac > frac ).
thf(satz39,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wvhlBlyiZ1/E---3.1_26363.p',satz39) ).
thf(e,axiom,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox2/tmp/tmp.wvhlBlyiZ1/E---3.1_26363.p',e) ).
thf(satz58,axiom,
! [X1: frac,X2: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wvhlBlyiZ1/E---3.1_26363.p',satz58) ).
thf(satz63b,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) )
=> ( eq @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.wvhlBlyiZ1/E---3.1_26363.p',satz63b) ).
thf(satz63e,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.wvhlBlyiZ1/E---3.1_26363.p',satz63e) ).
thf(c_0_5,plain,
! [X15: frac,X16: frac,X17: frac] :
( ~ ( eq @ X15 @ X16 )
| ~ ( eq @ X16 @ X17 )
| ( eq @ X15 @ X17 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz39])])]) ).
thf(c_0_6,plain,
! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X3 )
| ~ ( eq @ X1 @ X2 )
| ~ ( eq @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_8,plain,
! [X1: frac] :
( ( eq @ X1 @ ( pf @ z @ y ) )
| ~ ( eq @ X1 @ ( pf @ z @ x ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,plain,
! [X18: frac,X19: frac] : ( eq @ ( pf @ X18 @ X19 ) @ ( pf @ X19 @ X18 ) ),
inference(variable_rename,[status(thm)],[satz58]) ).
thf(c_0_10,plain,
! [X12: frac,X13: frac,X14: frac] :
( ~ ( eq @ ( pf @ X12 @ X14 ) @ ( pf @ X13 @ X14 ) )
| ( eq @ X12 @ X13 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz63b])])]) ).
thf(c_0_11,plain,
! [X1: frac,X2: frac] :
( ( eq @ X1 @ ( pf @ z @ y ) )
| ~ ( eq @ X2 @ ( pf @ z @ x ) )
| ~ ( eq @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
thf(c_0_12,plain,
! [X2: frac,X1: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X1: frac,X3: frac,X2: frac] :
( ( eq @ X1 @ X3 )
| ~ ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ( eq @ x @ y ),
inference(assume_negation,[status(cth)],[satz63e]) ).
thf(c_0_15,plain,
! [X1: frac] :
( ( eq @ X1 @ ( pf @ z @ y ) )
| ~ ( eq @ X1 @ ( pf @ x @ z ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
! [X1: frac] : ( eq @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ( eq @ x @ y ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X1: frac,X3: frac,X2: frac] :
( ( eq @ X1 @ ( pf @ X2 @ X3 ) )
| ~ ( eq @ X1 @ ( pf @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
thf(c_0_19,plain,
eq @ ( pf @ x @ z ) @ ( pf @ z @ y ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
~ ( eq @ x @ y ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( eq @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM759^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:55:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.wvhlBlyiZ1/E---3.1_26363.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % Starting sh4l with 300s (1) cores
% 0.07/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.07/0.25 % ho_unfolding_6 with pid 26377 completed with status 0
% 0.07/0.25 % Result found by ho_unfolding_6
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHUNF-FFSF22-SFFFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 26380 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHUNF-FFSF22-SFFFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 11
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 11
% 0.07/0.25 % Removed in clause preprocessing : 6
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 16
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 1
% 0.07/0.25 % ...remaining for further processing : 15
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 25
% 0.07/0.25 % ...of the previous two non-redundant : 17
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 25
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 6
% 0.07/0.25 % ...of those cached : 1
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 15
% 0.07/0.25 % Positive orientable unit clauses : 6
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 8
% 0.07/0.25 % Current number of unprocessed clauses: 5
% 0.07/0.25 % ...number of literals in the above : 11
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 19
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 19
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 2
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 8
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 775
% 0.07/0.26 % Search garbage collected termcells : 62
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.003 s
% 0.07/0.26 % System time : 0.003 s
% 0.07/0.26 % Total time : 0.006 s
% 0.07/0.26 % Maximum resident set size: 3632 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.004 s
% 0.07/0.26 % System time : 0.007 s
% 0.07/0.26 % Total time : 0.012 s
% 0.07/0.26 % Maximum resident set size: 4608 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------