%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM739^1 : 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 : n003.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 08:16:58 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 187 ( 29 ~; 20 |; 1 &; 126 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 5 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,
u: frac ).
thf(decl_27,type,
moref: frac > frac > $o ).
thf(decl_28,type,
eq: frac > frac > $o ).
thf(satz46,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',satz46) ).
thf(satz44,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X2 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( ( eq @ X3 @ X5 )
=> ( moref @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',satz44) ).
thf(m,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',m) ).
thf(f,axiom,
eq @ y @ u,
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',f) ).
thf(satz39,axiom,
! [X2: frac,X3: frac,X4: frac] :
( ( eq @ X2 @ X3 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',satz39) ).
thf(satz38,axiom,
! [X2: frac,X3: frac] :
( ( eq @ X2 @ X3 )
=> ( eq @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',satz38) ).
thf(e,axiom,
eq @ x @ z,
file('/export/starexec/sandbox/tmp/tmp.OFvRKJudjp/E---3.1_2455575.p',e) ).
thf(c_0_7,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(assume_negation,[status(cth)],[satz46]) ).
thf(c_0_8,plain,
! [X21: frac,X22: frac,X23: frac,X24: frac] :
( ~ ( moref @ X21 @ X22 )
| ~ ( eq @ X21 @ X23 )
| ~ ( eq @ X22 @ X24 )
| ( moref @ X23 @ X24 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz44])])]) ).
thf(c_0_9,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_10,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X4 @ X5 )
| ~ ( moref @ X2 @ X3 )
| ~ ( eq @ X2 @ X4 )
| ~ ( eq @ X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
eq @ y @ u,
inference(split_conjunct,[status(thm)],[f]) ).
thf(c_0_13,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ~ ( moref @ z @ u )
& ~ ( eq @ z @ u ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
thf(c_0_15,plain,
! [X3: frac,X2: frac] :
( ( moref @ X2 @ u )
| ~ ( moref @ X3 @ y )
| ~ ( eq @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X16: frac,X17: frac,X18: frac] :
( ~ ( eq @ X16 @ X17 )
| ~ ( eq @ X17 @ X18 )
| ( eq @ X16 @ X18 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz39])])]) ).
thf(c_0_18,plain,
! [X19: frac,X20: frac] :
( ~ ( eq @ X19 @ X20 )
| ( eq @ X20 @ X19 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz38])])]) ).
thf(c_0_19,negated_conjecture,
~ ( moref @ z @ u ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X2: frac] :
( ( eq @ x @ y )
| ( moref @ X2 @ u )
| ~ ( eq @ x @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,plain,
eq @ x @ z,
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_22,plain,
! [X2: frac,X3: frac,X4: frac] :
( ( eq @ X2 @ X4 )
| ~ ( eq @ X2 @ X3 )
| ~ ( eq @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X2: frac,X3: frac] :
( ( eq @ X3 @ X2 )
| ~ ( eq @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
eq @ x @ y,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
thf(c_0_25,plain,
! [X2: frac] :
( ( eq @ X2 @ z )
| ~ ( eq @ X2 @ x ) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
thf(c_0_26,negated_conjecture,
eq @ y @ x,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_27,negated_conjecture,
~ ( eq @ z @ u ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_28,plain,
! [X2: frac] :
( ( eq @ X2 @ u )
| ~ ( eq @ X2 @ y ) ),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
thf(c_0_29,negated_conjecture,
eq @ y @ z,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,negated_conjecture,
~ ( eq @ z @ y ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM739^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.15 % Computer : n003.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Sep 29 12:48:43 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.21 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.OFvRKJudjp/E---3.1_2455575.p
% 0.10/0.22 % Version: 3.5.1-ho
% 0.10/0.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.22 % Starting full_lambda_5 with 300s (1) cores
% 0.10/0.22 % Starting new_ho_10_unif with 300s (1) cores
% 0.10/0.22 % new_ho_10_unif with pid 2455591 completed with status 0
% 0.10/0.22 % Result found by new_ho_10_unif
% 0.10/0.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.22 % Starting full_lambda_5 with 300s (1) cores
% 0.10/0.22 % Starting new_ho_10_unif with 300s (1) cores
% 0.10/0.22 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.22 % No SInE strategy applied
% 0.10/0.22 % Search class: HGUNF-FFSS00-SFFFFFNN
% 0.10/0.22 % partial match(1): FGUNF-FFSS00-SFFFFFNN
% 0.10/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.22 % SubtermCWHack with pid 2455592 completed with status 0
% 0.10/0.22 % Result found by SubtermCWHack
% 0.10/0.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.22 % Starting full_lambda_5 with 300s (1) cores
% 0.10/0.22 % Starting new_ho_10_unif with 300s (1) cores
% 0.10/0.22 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.22 % No SInE strategy applied
% 0.10/0.22 % Search class: HGUNF-FFSS00-SFFFFFNN
% 0.10/0.22 % partial match(1): FGUNF-FFSS00-SFFFFFNN
% 0.10/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.22 % Preprocessing time : 0.001 s
% 0.10/0.22
% 0.10/0.22 % Proof found!
% 0.10/0.22 % SZS status Theorem
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22 % Parsed axioms : 15
% 0.10/0.22 % Removed by relevancy pruning/SinE : 0
% 0.10/0.22 % Initial clauses : 16
% 0.10/0.22 % Removed in clause preprocessing : 8
% 0.10/0.22 % Initial clauses in saturation : 8
% 0.10/0.22 % Processed clauses : 39
% 0.10/0.22 % ...of these trivial : 0
% 0.10/0.22 % ...subsumed : 2
% 0.10/0.22 % ...remaining for further processing : 37
% 0.10/0.22 % Other redundant clauses eliminated : 0
% 0.10/0.22 % Clauses deleted for lack of memory : 0
% 0.10/0.22 % Backward-subsumed : 0
% 0.10/0.22 % Backward-rewritten : 2
% 0.10/0.22 % Generated clauses : 82
% 0.10/0.22 % ...of the previous two non-redundant : 57
% 0.10/0.22 % ...aggressively subsumed : 0
% 0.10/0.22 % Contextual simplify-reflections : 0
% 0.10/0.22 % Paramodulations : 82
% 0.10/0.22 % Factorizations : 0
% 0.10/0.22 % NegExts : 0
% 0.10/0.23 % Equation resolutions : 0
% 0.10/0.23 % Disequality decompositions : 0
% 0.10/0.23 % Total rewrite steps : 14
% 0.10/0.23 % ...of those cached : 6
% 0.10/0.23 % Propositional unsat checks : 0
% 0.10/0.23 % Propositional check models : 0
% 0.10/0.23 % Propositional check unsatisfiable : 0
% 0.10/0.23 % Propositional clauses : 0
% 0.10/0.23 % Propositional clauses after purity: 0
% 0.10/0.23 % Propositional unsat core size : 0
% 0.10/0.23 % Propositional preprocessing time : 0.000
% 0.10/0.23 % Propositional encoding time : 0.000
% 0.10/0.23 % Propositional solver time : 0.000
% 0.10/0.23 % Success case prop preproc time : 0.000
% 0.10/0.23 % Success case prop encoding time : 0.000
% 0.10/0.23 % Success case prop solver time : 0.000
% 0.10/0.23 % Current number of processed clauses : 35
% 0.10/0.23 % Positive orientable unit clauses : 12
% 0.10/0.23 % Positive unorientable unit clauses: 0
% 0.10/0.23 % Negative unit clauses : 3
% 0.10/0.23 % Non-unit-clauses : 20
% 0.10/0.23 % Current number of unprocessed clauses: 26
% 0.10/0.23 % ...number of literals in the above : 75
% 0.10/0.23 % Current number of archived formulas : 0
% 0.10/0.23 % Current number of archived clauses : 2
% 0.10/0.23 % Clause-clause subsumption calls (NU) : 61
% 0.10/0.23 % Rec. Clause-clause subsumption calls : 59
% 0.10/0.23 % Non-unit clause-clause subsumptions : 2
% 0.10/0.23 % Unit Clause-clause subsumption calls : 4
% 0.10/0.23 % Rewrite failures with RHS unbound : 0
% 0.10/0.23 % BW rewrite match attempts : 1
% 0.10/0.23 % BW rewrite match successes : 1
% 0.10/0.23 % Condensation attempts : 0
% 0.10/0.23 % Condensation successes : 0
% 0.10/0.23 % Termbank termtop insertions : 1593
% 0.10/0.23 % Search garbage collected termcells : 111
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.005 s
% 0.10/0.23 % System time : 0.002 s
% 0.10/0.23 % Total time : 0.006 s
% 0.10/0.23 % Maximum resident set size: 3588 pages
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.006 s
% 0.10/0.23 % System time : 0.006 s
% 0.10/0.23 % Total time : 0.012 s
% 0.10/0.23 % Maximum resident set size: 4864 pages
% 0.10/0.23 % E exiting
%------------------------------------------------------------------------------