%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM686^1 : 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 : n020.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 08:16:49 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 244 ( 16 ~; 12 |; 0 &; 210 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 67 ( 23 ^; 44 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
z: nat ).
thf(decl_26,type,
u: nat ).
thf(decl_27,type,
some: ( nat > $o ) > $o ).
thf(decl_28,type,
diffprop: nat > nat > nat > $o ).
thf(decl_29,type,
pl: nat > nat > nat ).
thf(satz19a,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [X1: nat] : ( diffprop @ X3 @ X4 @ X1 ) )
=> ( some
@ ^ [X1: nat] : ( diffprop @ ( pl @ X3 @ X5 ) @ ( pl @ X4 @ X5 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',satz19a) ).
thf(satz15,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [X6: nat] : ( diffprop @ X4 @ X3 @ X6 ) )
=> ( ( some
@ ^ [X6: nat] : ( diffprop @ X5 @ X4 @ X6 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ X5 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',satz15) ).
thf(satz6,axiom,
! [X3: nat,X4: nat] :
( ( pl @ X3 @ X4 )
= ( pl @ X4 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',satz6) ).
thf(satz21,conjecture,
( some
@ ^ [X2: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',satz21) ).
thf(m,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ x @ y @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',m) ).
thf(n,axiom,
( some
@ ^ [X2: nat] : ( diffprop @ z @ u @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.9KSA3Ck3rE/E---3.1_995213.p',n) ).
thf(c_0_6,plain,
! [X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [Z0: nat] : ( diffprop @ X3 @ X4 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ X3 @ X5 ) @ ( pl @ X4 @ X5 ) @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[satz19a]) ).
thf(c_0_7,plain,
! [X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X3 @ Z0 ) )
=> ( ( some
@ ^ [Z0: nat] : ( diffprop @ X5 @ X4 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ X5 @ X3 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz15]) ).
thf(c_0_8,plain,
! [X18: nat,X19: nat,X20: nat] :
( ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X18 @ X19 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ X18 @ X20 ) @ ( pl @ X19 @ X20 ) @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_9,plain,
! [X21: nat,X22: nat] :
( ( pl @ X21 @ X22 )
= ( pl @ X22 @ X21 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_10,negated_conjecture,
~ ( some
@ ^ [X2: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ X2 ) ),
inference(assume_negation,[status(cth)],[satz21]) ).
thf(c_0_11,plain,
! [X15: nat,X16: nat,X17: nat] :
( ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X16 @ X15 @ Z0 ) )
| ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X17 @ X16 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ X17 @ X15 @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_12,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) )
| ~ ( some @ ( diffprop @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X2: nat,X1: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Z0 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])]) ).
thf(c_0_15,plain,
! [X3: nat,X2: nat,X1: nat] :
( ( some @ ( diffprop @ X3 @ X2 ) )
| ~ ( some @ ( diffprop @ X1 @ X2 ) )
| ~ ( some @ ( diffprop @ X3 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X2 @ X3 ) ) )
| ~ ( some @ ( diffprop @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Z0 ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X1: nat,X3: nat,X2: nat,X4: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X2 ) @ X3 ) )
| ~ ( some @ ( diffprop @ ( pl @ X4 @ X2 ) @ X3 ) )
| ~ ( some @ ( diffprop @ X1 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
thf(c_0_19,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X1 @ X3 ) ) )
| ~ ( some @ ( diffprop @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
thf(c_0_20,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ x @ y @ Z0 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_21,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ z @ u @ Z0 ) ),
inference(fof_simplification,[status(thm)],[n]) ).
thf(c_0_22,negated_conjecture,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X2 ) @ ( pl @ X3 @ X4 ) ) )
| ~ ( some @ ( diffprop @ X1 @ X3 ) )
| ~ ( some @ ( diffprop @ X2 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
some @ ( diffprop @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_25,plain,
some @ ( diffprop @ z @ u ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM686^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n020.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 12:38:49 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.22 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.9KSA3Ck3rE/E---3.1_995213.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % partial match(1): HSMSSMSSSSSNSSN
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSLNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_11 with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting new_ho_9 with 300s (1) cores
% 0.08/0.25 % Starting ho_unfolding_4 with 300s (1) cores
% 0.08/0.25 % new_ho_11 with pid 995226 completed with status 0
% 0.08/0.25 % Result found by new_ho_11
% 0.08/0.25 % partial match(1): HSMSSMSSSSSNSSN
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSLNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_11 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUSF-FFSF22-SSSFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.25 % Starting new_ho_11 with 151s (1) cores
% 0.08/0.25 % Starting sh5l with 136s (1) cores
% 0.08/0.25 % Starting new_bool_1 with 136s (1) cores
% 0.08/0.25 % Starting new_bool_2 with 136s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 995231 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % partial match(1): HSMSSMSSSSSNSSN
% 0.08/0.25 % Preprocessing class: HSMSSMSSSSLNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_11 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUSF-FFSF22-SSSFFFNN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (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 : 0
% 0.08/0.25 % Initial clauses : 14
% 0.08/0.25 % Removed in clause preprocessing : 8
% 0.08/0.25 % Initial clauses in saturation : 6
% 0.08/0.25 % Processed clauses : 71
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 43
% 0.08/0.25 % ...remaining for further processing : 28
% 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 : 170
% 0.08/0.25 % ...of the previous two non-redundant : 165
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 170
% 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 : 28
% 0.08/0.25 % Positive orientable unit clauses : 2
% 0.08/0.25 % Positive unorientable unit clauses: 1
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 24
% 0.08/0.25 % Current number of unprocessed clauses: 93
% 0.08/0.25 % ...number of literals in the above : 286
% 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) : 408
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 408
% 0.08/0.25 % Non-unit clause-clause subsumptions : 43
% 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 : 3162
% 0.08/0.25 % Search garbage collected termcells : 117
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.003 s
% 0.08/0.25 % Total time : 0.008 s
% 0.08/0.25 % Maximum resident set size: 3640 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.016 s
% 0.08/0.25 % System time : 0.011 s
% 0.08/0.25 % Total time : 0.027 s
% 0.08/0.25 % Maximum resident set size: 4608 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------