%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM766^1 : 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 : n013.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 08:17:04 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 366 ( 25 ~; 11 |; 0 &; 326 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
frac: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_23,type,
x: frac ).
thf(decl_24,type,
y: frac ).
thf(decl_25,type,
ts: nat > nat > nat ).
thf(decl_26,type,
num: frac > nat ).
thf(decl_27,type,
den: frac > nat ).
thf(decl_28,type,
pl: nat > nat > nat ).
thf(decl_29,type,
eq: frac > frac > $o ).
thf(decl_30,type,
pf: frac > frac > frac ).
thf(decl_31,type,
fr: nat > nat > frac ).
thf(decl_34,type,
esk1_0: nat ).
thf(m,axiom,
~ ! [X1: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',m) ).
thf(satz39,axiom,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ X5 @ X6 )
=> ( ( eq @ X6 @ X7 )
=> ( eq @ X5 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz39) ).
thf(satz40a,axiom,
! [X18: frac,X13: nat] : ( eq @ ( fr @ ( ts @ ( num @ X18 ) @ X13 ) @ ( ts @ ( den @ X18 ) @ X13 ) ) @ X18 ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz40a) ).
thf(satz57,axiom,
! [X15: nat,X16: nat,X13: nat] : ( eq @ ( pf @ ( fr @ X15 @ X13 ) @ ( fr @ X16 @ X13 ) ) @ ( fr @ ( pl @ X15 @ X16 ) @ X13 ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz57) ).
thf(satz56,axiom,
! [X8: frac,X9: frac,X10: frac,X11: frac] :
( ( eq @ X8 @ X9 )
=> ( ( eq @ X10 @ X11 )
=> ( eq @ ( pf @ X8 @ X10 ) @ ( pf @ X9 @ X11 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz56) ).
thf(satz37,axiom,
! [X14: frac] : ( eq @ X14 @ X14 ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz37) ).
thf(satz40,axiom,
! [X12: frac,X13: nat] : ( eq @ X12 @ ( fr @ ( ts @ ( num @ X12 ) @ X13 ) @ ( ts @ ( den @ X12 ) @ X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz40) ).
thf(satz29,axiom,
! [X2: nat,X3: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz29) ).
thf(satz67a,conjecture,
~ ! [X19: frac] :
~ ( eq @ ( pf @ y @ X19 ) @ x ),
file('/export/starexec/sandbox2/tmp/tmp.S4nQgqlexX/E---3.1_2059054.p',satz67a) ).
thf(c_0_9,plain,
~ ! [X1: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_10,plain,
! [X46: frac,X47: frac,X48: frac] :
( ~ ( eq @ X46 @ X47 )
| ~ ( eq @ X47 @ X48 )
| ( eq @ X46 @ X48 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz39])])]) ).
thf(c_0_11,plain,
! [X63: frac,X64: nat] : ( eq @ ( fr @ ( ts @ ( num @ X63 ) @ X64 ) @ ( ts @ ( den @ X63 ) @ X64 ) ) @ X63 ),
inference(variable_rename,[status(thm)],[satz40a]) ).
thf(c_0_12,plain,
! [X58: nat,X59: nat,X60: nat] : ( eq @ ( pf @ ( fr @ X58 @ X60 ) @ ( fr @ X59 @ X60 ) ) @ ( fr @ ( pl @ X58 @ X59 ) @ X60 ) ),
inference(variable_rename,[status(thm)],[satz57]) ).
thf(c_0_13,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ esk1_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_14,plain,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ X5 @ X7 )
| ~ ( eq @ X5 @ X6 )
| ~ ( eq @ X6 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: nat,X5: frac] : ( eq @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: nat,X3: nat,X2: nat] : ( eq @ ( pf @ ( fr @ X1 @ X2 ) @ ( fr @ X3 @ X2 ) ) @ ( fr @ ( pl @ X1 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
! [X49: frac,X50: frac,X51: frac,X52: frac] :
( ~ ( eq @ X49 @ X50 )
| ~ ( eq @ X51 @ X52 )
| ( eq @ ( pf @ X49 @ X51 ) @ ( pf @ X50 @ X52 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).
thf(c_0_19,plain,
! [X55: frac] : ( eq @ X55 @ X55 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_20,plain,
! [X53: frac,X54: nat] : ( eq @ X53 @ ( fr @ ( ts @ ( num @ X53 ) @ X54 ) @ ( ts @ ( den @ X53 ) @ X54 ) ) ),
inference(variable_rename,[status(thm)],[satz40]) ).
thf(c_0_21,plain,
! [X56: nat,X57: nat] :
( ( ts @ X56 @ X57 )
= ( ts @ X57 @ X56 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_22,negated_conjecture,
~ ~ ! [X19: frac] :
~ ( eq @ ( pf @ y @ X19 ) @ x ),
inference(assume_negation,[status(cth)],[satz67a]) ).
thf(c_0_23,plain,
! [X6: frac,X5: frac,X1: nat] :
( ( eq @ X5 @ X6 )
| ~ ( eq @ X5 @ ( fr @ ( ts @ ( num @ X6 ) @ X1 ) @ ( ts @ ( den @ X6 ) @ X1 ) ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_24,plain,
! [X1: nat] : ( eq @ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) @ ( fr @ esk1_0 @ X1 ) ) @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_25,plain,
! [X5: frac,X6: frac,X7: frac,X8: frac] :
( ( eq @ ( pf @ X5 @ X7 ) @ ( pf @ X6 @ X8 ) )
| ~ ( eq @ X5 @ X6 )
| ~ ( eq @ X7 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,plain,
! [X5: frac] : ( eq @ X5 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
! [X5: frac,X1: nat] : ( eq @ X5 @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,negated_conjecture,
~ ~ ! [X19: frac] :
~ ( eq @ ( pf @ y @ X19 ) @ x ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
thf(c_0_30,plain,
eq @ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ esk1_0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_31,plain,
! [X5: frac,X6: frac,X7: frac] :
( ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ X7 @ X6 ) )
| ~ ( eq @ X5 @ X7 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_32,plain,
! [X1: nat,X5: frac] : ( eq @ X5 @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ X1 @ ( den @ X5 ) ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_33,negated_conjecture,
! [X65: frac] :
~ ( eq @ ( pf @ y @ X65 ) @ x ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
thf(c_0_34,plain,
! [X5: frac] :
( ( eq @ X5 @ x )
| ~ ( eq @ X5 @ ( pf @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ esk1_0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
thf(c_0_35,plain,
! [X1: nat,X5: frac,X6: frac] : ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ X1 @ ( den @ X5 ) ) ) @ X6 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X5: frac] :
~ ( eq @ ( pf @ y @ X5 ) @ x ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM766^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:53:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.S4nQgqlexX/E---3.1_2059054.p
% 0.23/0.33 % Version: 3.5.1-ho
% 0.23/0.33 % partial match(1): HSMSSMSSSSSNSFA
% 0.23/0.33 % Preprocessing class: HSMSSMSSSSSCSFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_14 with 1200s (4) cores
% 0.23/0.33 % Starting new_ho_13 with 600s (2) cores
% 0.23/0.33 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.23/0.33 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.33 % new_ho_13 with pid 2059068 completed with status 0
% 0.23/0.33 % Result found by new_ho_13
% 0.23/0.33 % partial match(1): HSMSSMSSSSSNSFA
% 0.23/0.33 % Preprocessing class: HSMSSMSSSSSCSFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_14 with 1200s (4) cores
% 0.23/0.33 % Starting new_ho_13 with 600s (2) cores
% 0.23/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.33 % No SInE strategy applied
% 0.23/0.33 % Search class: HHUSM-FFSF21-MSFFFFBN
% 0.23/0.33 % partial match(2): HHUSM-FFSF21-MSFSMFBN
% 0.23/0.33 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.23/0.33 % Starting SubtermCWHack with 55s (1) cores
% 0.23/0.33 % Starting new_ho_13 with 61s (1) cores
% 0.23/0.33 % new_ho_13 with pid 2059074 completed with status 0
% 0.23/0.33 % Result found by new_ho_13
% 0.23/0.33 % partial match(1): HSMSSMSSSSSNSFA
% 0.23/0.33 % Preprocessing class: HSMSSMSSSSSCSFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_14 with 1200s (4) cores
% 0.23/0.33 % Starting new_ho_13 with 600s (2) cores
% 0.23/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.33 % No SInE strategy applied
% 0.23/0.33 % Search class: HHUSM-FFSF21-MSFFFFBN
% 0.23/0.33 % partial match(2): HHUSM-FFSF21-MSFSMFBN
% 0.23/0.33 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.23/0.33 % Starting SubtermCWHack with 55s (1) cores
% 0.23/0.33 % Starting new_ho_13 with 61s (1) cores
% 0.23/0.33 % Preprocessing time : 0.001 s
% 0.23/0.33 % Presaturation interreduction done
% 0.23/0.33
% 0.23/0.33 % Proof found!
% 0.23/0.33 % SZS status Theorem
% 0.23/0.33 % SZS output start CNFRefutation
% See solution above
% 0.23/0.34 % Parsed axioms : 24
% 0.23/0.34 % Removed by relevancy pruning/SinE : 0
% 0.23/0.34 % Initial clauses : 24
% 0.23/0.34 % Removed in clause preprocessing : 13
% 0.23/0.34 % Initial clauses in saturation : 11
% 0.23/0.34 % Processed clauses : 261
% 0.23/0.34 % ...of these trivial : 51
% 0.23/0.34 % ...subsumed : 74
% 0.23/0.34 % ...remaining for further processing : 136
% 0.23/0.34 % Other redundant clauses eliminated : 0
% 0.23/0.34 % Clauses deleted for lack of memory : 0
% 0.23/0.34 % Backward-subsumed : 0
% 0.23/0.34 % Backward-rewritten : 0
% 0.23/0.34 % Generated clauses : 2975
% 0.23/0.34 % ...of the previous two non-redundant : 2675
% 0.23/0.34 % ...aggressively subsumed : 0
% 0.23/0.34 % Contextual simplify-reflections : 0
% 0.23/0.34 % Paramodulations : 2975
% 0.23/0.34 % Factorizations : 0
% 0.23/0.34 % NegExts : 0
% 0.23/0.34 % Equation resolutions : 0
% 0.23/0.34 % Disequality decompositions : 0
% 0.23/0.34 % Total rewrite steps : 356
% 0.23/0.34 % ...of those cached : 309
% 0.23/0.34 % Propositional unsat checks : 0
% 0.23/0.34 % Propositional check models : 0
% 0.23/0.34 % Propositional check unsatisfiable : 0
% 0.23/0.34 % Propositional clauses : 0
% 0.23/0.34 % Propositional clauses after purity: 0
% 0.23/0.34 % Propositional unsat core size : 0
% 0.23/0.34 % Propositional preprocessing time : 0.000
% 0.23/0.34 % Propositional encoding time : 0.000
% 0.23/0.34 % Propositional solver time : 0.000
% 0.23/0.34 % Success case prop preproc time : 0.000
% 0.23/0.34 % Success case prop encoding time : 0.000
% 0.23/0.34 % Success case prop solver time : 0.000
% 0.23/0.34 % Current number of processed clauses : 125
% 0.23/0.34 % Positive orientable unit clauses : 49
% 0.23/0.34 % Positive unorientable unit clauses: 1
% 0.23/0.34 % Negative unit clauses : 1
% 0.23/0.34 % Non-unit-clauses : 74
% 0.23/0.34 % Current number of unprocessed clauses: 2420
% 0.23/0.34 % ...number of literals in the above : 2472
% 0.23/0.34 % Current number of archived formulas : 0
% 0.23/0.34 % Current number of archived clauses : 11
% 0.23/0.34 % Clause-clause subsumption calls (NU) : 2632
% 0.23/0.34 % Rec. Clause-clause subsumption calls : 2158
% 0.23/0.34 % Non-unit clause-clause subsumptions : 74
% 0.23/0.34 % Unit Clause-clause subsumption calls : 261
% 0.23/0.34 % Rewrite failures with RHS unbound : 0
% 0.23/0.34 % BW rewrite match attempts : 226
% 0.23/0.34 % BW rewrite match successes : 0
% 0.23/0.34 % Condensation attempts : 0
% 0.23/0.34 % Condensation successes : 0
% 0.23/0.34 % Termbank termtop insertions : 80995
% 0.23/0.34 % Search garbage collected termcells : 184
% 0.23/0.34
% 0.23/0.34 % -------------------------------------------------
% 0.23/0.34 % User time : 0.067 s
% 0.23/0.34 % System time : 0.007 s
% 0.23/0.34 % Total time : 0.074 s
% 0.23/0.34 % Maximum resident set size: 3656 pages
% 0.23/0.34
% 0.23/0.34 % -------------------------------------------------
% 0.23/0.34 % User time : 0.130 s
% 0.23/0.34 % System time : 0.020 s
% 0.23/0.34 % Total time : 0.150 s
% 0.23/0.34 % Maximum resident set size: 4864 pages
% 0.23/0.34 % E exiting
%------------------------------------------------------------------------------