%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM721^1 : 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 : 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 08:16:56 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 8 ~; 4 |; 0 &; 122 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 17 ^; 16 !; 0 ?; 33 :)
% 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,
ts: nat > nat > nat ).
thf(satz34a,conjecture,
( some
@ ^ [X1: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.aOEsCwq96B/E---3.1_662635.p',satz34a) ).
thf(satz34,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [X5: nat] : ( diffprop @ X2 @ X3 @ X5 ) )
=> ( ( some
@ ^ [X6: nat] : ( diffprop @ X4 @ X5 @ X6 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ ( ts @ X2 @ X4 ) @ ( ts @ X3 @ X5 ) @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aOEsCwq96B/E---3.1_662635.p',satz34) ).
thf(k,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ u @ z @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.aOEsCwq96B/E---3.1_662635.p',k) ).
thf(l,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ y @ x @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.aOEsCwq96B/E---3.1_662635.p',l) ).
thf(c_0_4,negated_conjecture,
~ ( some
@ ^ [X1: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X1 ) ),
inference(assume_negation,[status(cth)],[satz34a]) ).
thf(c_0_5,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Z0 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_6,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( some
@ ^ [Z0: nat] : ( diffprop @ X2 @ X3 @ Z0 ) )
=> ( ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X5 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ ( ts @ X2 @ X4 ) @ ( ts @ X3 @ X5 ) @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz34]) ).
thf(c_0_7,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Z0 ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X11: nat,X12: nat,X13: nat,X14: nat] :
( ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X11 @ X12 @ Z0 ) )
| ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X13 @ X14 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ ( ts @ X11 @ X13 ) @ ( ts @ X12 @ X14 ) @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_9,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ u @ z @ Z0 ) ),
inference(fof_simplification,[status(thm)],[k]) ).
thf(c_0_10,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ y @ x @ Z0 ) ),
inference(fof_simplification,[status(thm)],[l]) ).
thf(c_0_11,negated_conjecture,
~ ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( some @ ( diffprop @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) ) )
| ~ ( some @ ( diffprop @ X1 @ X2 ) )
| ~ ( some @ ( diffprop @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
some @ ( diffprop @ u @ z ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
some @ ( diffprop @ y @ x ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM721^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n006.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 12:44:54 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 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.aOEsCwq96B/E---3.1_662635.p
% 0.08/0.23 % Version: 3.5.1-ho
% 0.08/0.23 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting sh3 with 1500s (5) cores
% 0.08/0.23 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.08/0.23 % Starting sh2lt with 300s (1) cores
% 0.08/0.23 % Starting ho_unfolding_1 with 300s (1) cores
% 0.08/0.23 % sh3 with pid 662648 completed with status 0
% 0.08/0.23 % Result found by sh3
% 0.08/0.23 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting sh3 with 1500s (5) cores
% 0.08/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HHUNF-FFSF22-SSSFFFNN
% 0.08/0.23 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.23 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.23 % Starting sh3 with 151s (1) cores
% 0.08/0.23 % Starting sh5l with 136s (1) cores
% 0.08/0.23 % Starting new_bool_1 with 136s (1) cores
% 0.08/0.23 % Starting new_bool_2 with 136s (1) cores
% 0.08/0.23 % SubtermCWHack with pid 662652 completed with status 0
% 0.08/0.23 % Result found by SubtermCWHack
% 0.08/0.23 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting sh3 with 1500s (5) cores
% 0.08/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HHUNF-FFSF22-SSSFFFNN
% 0.08/0.23 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.23 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.23 % Preprocessing time : 0.001 s
% 0.08/0.23
% 0.08/0.23 % Proof found!
% 0.08/0.23 % SZS status Theorem
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23 % Parsed axioms : 12
% 0.08/0.23 % Removed by relevancy pruning/SinE : 0
% 0.08/0.23 % Initial clauses : 12
% 0.08/0.23 % Removed in clause preprocessing : 8
% 0.08/0.23 % Initial clauses in saturation : 4
% 0.08/0.23 % Processed clauses : 4
% 0.08/0.23 % ...of these trivial : 0
% 0.08/0.23 % ...subsumed : 0
% 0.08/0.23 % ...remaining for further processing : 4
% 0.08/0.23 % Other redundant clauses eliminated : 0
% 0.08/0.23 % Clauses deleted for lack of memory : 0
% 0.08/0.23 % Backward-subsumed : 0
% 0.08/0.23 % Backward-rewritten : 0
% 0.08/0.23 % Generated clauses : 1
% 0.08/0.23 % ...of the previous two non-redundant : 0
% 0.08/0.23 % ...aggressively subsumed : 0
% 0.08/0.23 % Contextual simplify-reflections : 0
% 0.08/0.23 % Paramodulations : 1
% 0.08/0.23 % Factorizations : 0
% 0.08/0.23 % NegExts : 0
% 0.08/0.23 % Equation resolutions : 0
% 0.08/0.23 % Disequality decompositions : 0
% 0.08/0.23 % Total rewrite steps : 2
% 0.08/0.23 % ...of those cached : 0
% 0.08/0.23 % Propositional unsat checks : 0
% 0.08/0.23 % Propositional check models : 0
% 0.08/0.23 % Propositional check unsatisfiable : 0
% 0.08/0.23 % Propositional clauses : 0
% 0.08/0.23 % Propositional clauses after purity: 0
% 0.08/0.23 % Propositional unsat core size : 0
% 0.08/0.23 % Propositional preprocessing time : 0.000
% 0.08/0.23 % Propositional encoding time : 0.000
% 0.08/0.23 % Propositional solver time : 0.000
% 0.08/0.23 % Success case prop preproc time : 0.000
% 0.08/0.23 % Success case prop encoding time : 0.000
% 0.08/0.23 % Success case prop solver time : 0.000
% 0.08/0.23 % Current number of processed clauses : 4
% 0.08/0.23 % Positive orientable unit clauses : 2
% 0.08/0.23 % Positive unorientable unit clauses: 0
% 0.08/0.23 % Negative unit clauses : 1
% 0.08/0.23 % Non-unit-clauses : 1
% 0.08/0.23 % Current number of unprocessed clauses: 0
% 0.08/0.23 % ...number of literals in the above : 0
% 0.08/0.23 % Current number of archived formulas : 0
% 0.08/0.23 % Current number of archived clauses : 0
% 0.08/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.23 % Non-unit clause-clause subsumptions : 0
% 0.08/0.23 % Unit Clause-clause subsumption calls : 0
% 0.08/0.23 % Rewrite failures with RHS unbound : 0
% 0.08/0.23 % BW rewrite match attempts : 0
% 0.08/0.23 % BW rewrite match successes : 0
% 0.08/0.23 % Condensation attempts : 0
% 0.08/0.23 % Condensation successes : 0
% 0.08/0.23 % Termbank termtop insertions : 565
% 0.08/0.23 % Search garbage collected termcells : 76
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.004 s
% 0.08/0.24 % System time : 0.001 s
% 0.08/0.24 % Total time : 0.005 s
% 0.08/0.24 % Maximum resident set size: 3636 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.012 s
% 0.08/0.24 % System time : 0.008 s
% 0.08/0.24 % Total time : 0.020 s
% 0.08/0.24 % Maximum resident set size: 4864 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------