%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM754^1 : 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 : n006.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 08:17:01 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 185 ( 21 ~; 17 |; 0 &; 142 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 43 !; 0 ?; 43 :)
% 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,
eq: frac > frac > $o ).
thf(decl_28,type,
moref: frac > frac > $o ).
thf(decl_29,type,
pf: frac > frac > frac ).
thf(satz44,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( moref @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',satz44) ).
thf(satz58,axiom,
! [X1: frac,X2: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',satz58) ).
thf(satz62h,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',satz62h) ).
thf(satz62g,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( eq @ X1 @ X2 )
=> ( ( moref @ X3 @ X4 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',satz62g) ).
thf(e,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',e) ).
thf(m,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/tmp/tmp.G0Js4VvWKA/E---3.1_665849.p',m) ).
thf(c_0_6,plain,
! [X15: frac,X16: frac,X17: frac,X18: frac] :
( ~ ( moref @ X15 @ X16 )
| ~ ( eq @ X15 @ X17 )
| ~ ( eq @ X16 @ X18 )
| ( moref @ X17 @ X18 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz44])])]) ).
thf(c_0_7,plain,
! [X23: frac,X24: frac] : ( eq @ ( pf @ X23 @ X24 ) @ ( pf @ X24 @ X23 ) ),
inference(variable_rename,[status(thm)],[satz58]) ).
thf(c_0_8,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(assume_negation,[status(cth)],[satz62h]) ).
thf(c_0_9,plain,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ X3 @ X4 )
| ~ ( moref @ X1 @ X2 )
| ~ ( eq @ X1 @ X3 )
| ~ ( eq @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X2: frac,X1: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X19: frac,X20: frac,X21: frac,X22: frac] :
( ~ ( eq @ X19 @ X20 )
| ~ ( moref @ X21 @ X22 )
| ( moref @ ( pf @ X19 @ X21 ) @ ( pf @ X20 @ X22 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz62g])])]) ).
thf(c_0_12,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X2: frac,X4: frac,X3: frac,X1: frac] :
( ( moref @ X1 @ ( pf @ X2 @ X3 ) )
| ~ ( moref @ X4 @ ( pf @ X3 @ X2 ) )
| ~ ( eq @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) )
| ~ ( eq @ X1 @ X2 )
| ~ ( moref @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X1: frac,X3: frac,X5: frac,X4: frac,X2: frac] :
( ( moref @ X1 @ ( pf @ X2 @ X3 ) )
| ~ ( eq @ ( pf @ X4 @ X5 ) @ X1 )
| ~ ( eq @ X4 @ X3 )
| ~ ( moref @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X2: frac,X1: frac,X4: frac,X3: frac] :
( ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X3 @ X4 ) )
| ~ ( eq @ X2 @ X4 )
| ~ ( moref @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
thf(c_0_19,plain,
eq @ x @ y,
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_20,plain,
moref @ z @ u,
inference(split_conjunct,[status(thm)],[m]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM754^1 : 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 : n006.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 12:50:54 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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.G0Js4VvWKA/E---3.1_665849.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 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 new_bool_1 with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.25 % Starting new_ho_10_unif with 300s (1) cores
% 0.08/0.25 % new_bool_1 with pid 665863 completed with status 0
% 0.08/0.25 % Result found by new_bool_1
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 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 new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HHUNF-FFSF22-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 665866 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 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 new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HHUNF-FFSF22-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 : 14
% 0.08/0.25 % Removed by relevancy pruning/SinE : 8
% 0.08/0.25 % Initial clauses : 6
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 6
% 0.08/0.25 % Processed clauses : 13
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 13
% 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 : 0
% 0.08/0.25 % Generated clauses : 9
% 0.08/0.25 % ...of the previous two non-redundant : 8
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 9
% 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 : 2
% 0.08/0.25 % ...of those cached : 0
% 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 : 13
% 0.08/0.25 % Positive orientable unit clauses : 3
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 9
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 0
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 6
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 5
% 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 : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 683
% 0.08/0.25 % Search garbage collected termcells : 90
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.005 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.006 s
% 0.08/0.25 % Total time : 0.011 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------