%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET716^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:22:18 AM UTC 2026
% Result : Theorem 0.26s 0.27s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 10 ~; 6 |; 6 &; 73 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 5 ^; 35 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_26,type,
fun_injective: ( $i > $i ) > $o ).
thf(decl_31,type,
esk1_0: $i > $i ).
thf(decl_32,type,
esk2_0: $i > $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(thm,conjecture,
! [X1: $i > $i,X5: $i > $i] :
( ( ( fun_injective @ X1 )
& ( fun_injective @ X5 ) )
=> ( fun_injective @ ( fun_composition @ X1 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XMfhvPOaS1/E---3.1_1299663.p',thm) ).
thf(fun_injective,axiom,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X4: $i,X3: $i] :
( ( ( X1 @ X4 )
= ( X1 @ X3 ) )
=> ( X4 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XMfhvPOaS1/E---3.1_1299663.p',fun_injective) ).
thf(fun_composition,axiom,
( fun_composition
= ( ^ [X1: $i > $i,X5: $i > $i,X4: $i] : ( X5 @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XMfhvPOaS1/E---3.1_1299663.p',fun_composition) ).
thf(c_0_3,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i] :
( ( ( fun_injective @ X1 )
& ( fun_injective @ X5 ) )
=> ( fun_injective @ ( fun_composition @ X1 @ X5 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( fun_injective
= ( ^ [Z0: $i > $i] :
! [X4: $i,X3: $i] :
( ( ( Z0 @ X4 )
= ( Z0 @ X3 ) )
=> ( X4 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_injective]) ).
thf(c_0_5,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i] :
( ( ! [X14: $i,X15: $i] :
( ( ( X1 @ X14 )
= ( X1 @ X15 ) )
=> ( X14 = X15 ) )
& ! [X16: $i,X17: $i] :
( ( ( X5 @ X16 )
= ( X5 @ X17 ) )
=> ( X16 = X17 ) ) )
=> ! [X18: $i,X19: $i] :
( ( ( fun_composition @ X1 @ X5 @ X18 )
= ( fun_composition @ X1 @ X5 @ X19 ) )
=> ( X18 = X19 ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,plain,
! [X20: $i > $i,X21: $i > $i,X22: $i] :
( ( fun_composition @ X20 @ X21 @ X22 )
= ( X21 @ ( X20 @ X22 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fun_composition])]) ).
thf(c_0_7,negated_conjecture,
! [X28: $i,X29: $i,X30: $i,X31: $i] :
( ( ( ( esk1_0 @ X28 )
!= ( esk1_0 @ X29 ) )
| ( X28 = X29 ) )
& ( ( ( esk2_0 @ X30 )
!= ( esk2_0 @ X31 ) )
| ( X30 = X31 ) )
& ( ( fun_composition @ esk1_0 @ esk2_0 @ esk3_0 )
= ( fun_composition @ esk1_0 @ esk2_0 @ esk4_0 ) )
& ( esk3_0 != esk4_0 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
thf(c_0_8,plain,
! [X23: $i > $i,X24: $i > $i,X25: $i] :
( ( fun_composition @ X23 @ X24 @ X25 )
= ( X24 @ ( X23 @ X25 ) ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( fun_composition @ esk1_0 @ esk2_0 @ esk3_0 )
= ( fun_composition @ esk1_0 @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: $i > $i,X5: $i > $i,X3: $i] :
( ( fun_composition @ X1 @ X5 @ X3 )
= ( X5 @ ( X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X4: $i] :
( ( X3 = X4 )
| ( ( esk2_0 @ X3 )
!= ( esk2_0 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
( ( esk2_0 @ ( esk1_0 @ esk3_0 ) )
= ( esk2_0 @ ( esk1_0 @ esk4_0 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i] :
( ( ( esk1_0 @ esk3_0 )
= X3 )
| ( ( esk2_0 @ ( esk1_0 @ esk4_0 ) )
!= ( esk2_0 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i,X4: $i] :
( ( X3 = X4 )
| ( ( esk1_0 @ X3 )
!= ( esk1_0 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,negated_conjecture,
( ( esk1_0 @ esk3_0 )
= ( esk1_0 @ esk4_0 ) ),
inference(er,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i] :
( ( esk3_0 = X3 )
| ( ( esk1_0 @ esk4_0 )
!= ( esk1_0 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET716^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.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 13:40:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.XMfhvPOaS1/E---3.1_1299663.p
% 0.26/0.27 % Version: 3.5.1-ho
% 0.26/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.26/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.26/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.27 % Starting sh1l with 300s (1) cores
% 0.26/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.26/0.27 % post_as_ho1 with pid 1299677 completed with status 0
% 0.26/0.27 % Result found by post_as_ho1
% 0.26/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.26/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.26/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.27 % No SInE strategy applied
% 0.26/0.27 % Search class: HHUPF-FFSF33-SHSSMSNN
% 0.26/0.27 % partial match(4): HHUNF-FFSF00-SHSSMFNN
% 0.26/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.27 % SubtermCWHack with pid 1299682 completed with status 0
% 0.26/0.27 % Result found by SubtermCWHack
% 0.26/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.26/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.26/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.27 % No SInE strategy applied
% 0.26/0.27 % Search class: HHUPF-FFSF33-SHSSMSNN
% 0.26/0.27 % partial match(4): HHUNF-FFSF00-SHSSMFNN
% 0.26/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.27 % Preprocessing time : 0.001 s
% 0.26/0.27
% 0.26/0.27 % Proof found!
% 0.26/0.27 % SZS status Theorem
% 0.26/0.27 % SZS output start CNFRefutation
% See solution above
% 0.26/0.27 % Parsed axioms : 17
% 0.26/0.27 % Removed by relevancy pruning/SinE : 0
% 0.26/0.27 % Initial clauses : 13
% 0.26/0.27 % Removed in clause preprocessing : 8
% 0.26/0.27 % Initial clauses in saturation : 5
% 0.26/0.27 % Processed clauses : 8
% 0.26/0.27 % ...of these trivial : 0
% 0.26/0.27 % ...subsumed : 0
% 0.26/0.27 % ...remaining for further processing : 8
% 0.26/0.27 % Other redundant clauses eliminated : 0
% 0.26/0.27 % Clauses deleted for lack of memory : 0
% 0.26/0.27 % Backward-subsumed : 0
% 0.26/0.27 % Backward-rewritten : 2
% 0.26/0.27 % Generated clauses : 8
% 0.26/0.27 % ...of the previous two non-redundant : 6
% 0.26/0.27 % ...aggressively subsumed : 0
% 0.26/0.27 % Contextual simplify-reflections : 0
% 0.26/0.27 % Paramodulations : 4
% 0.26/0.27 % Factorizations : 0
% 0.26/0.27 % NegExts : 0
% 0.26/0.27 % Equation resolutions : 4
% 0.26/0.27 % Disequality decompositions : 0
% 0.26/0.27 % Total rewrite steps : 4
% 0.26/0.27 % ...of those cached : 1
% 0.26/0.27 % Propositional unsat checks : 0
% 0.26/0.27 % Propositional check models : 0
% 0.26/0.27 % Propositional check unsatisfiable : 0
% 0.26/0.27 % Propositional clauses : 0
% 0.26/0.27 % Propositional clauses after purity: 0
% 0.26/0.27 % Propositional unsat core size : 0
% 0.26/0.27 % Propositional preprocessing time : 0.000
% 0.26/0.27 % Propositional encoding time : 0.000
% 0.26/0.27 % Propositional solver time : 0.000
% 0.26/0.27 % Success case prop preproc time : 0.000
% 0.26/0.27 % Success case prop encoding time : 0.000
% 0.26/0.27 % Success case prop solver time : 0.000
% 0.26/0.27 % Current number of processed clauses : 6
% 0.26/0.27 % Positive orientable unit clauses : 2
% 0.26/0.27 % Positive unorientable unit clauses: 0
% 0.26/0.27 % Negative unit clauses : 1
% 0.26/0.27 % Non-unit-clauses : 3
% 0.26/0.27 % Current number of unprocessed clauses: 3
% 0.26/0.27 % ...number of literals in the above : 6
% 0.26/0.27 % Current number of archived formulas : 0
% 0.26/0.27 % Current number of archived clauses : 2
% 0.26/0.27 % Clause-clause subsumption calls (NU) : 2
% 0.26/0.27 % Rec. Clause-clause subsumption calls : 2
% 0.26/0.27 % Non-unit clause-clause subsumptions : 0
% 0.26/0.27 % Unit Clause-clause subsumption calls : 0
% 0.26/0.27 % Rewrite failures with RHS unbound : 0
% 0.26/0.27 % BW rewrite match attempts : 1
% 0.26/0.27 % BW rewrite match successes : 1
% 0.26/0.27 % Condensation attempts : 0
% 0.26/0.27 % Condensation successes : 0
% 0.26/0.27 % Termbank termtop insertions : 881
% 0.26/0.27 % Search garbage collected termcells : 191
% 0.26/0.27
% 0.26/0.27 % -------------------------------------------------
% 0.26/0.27 % User time : 0.004 s
% 0.26/0.27 % System time : 0.001 s
% 0.26/0.27 % Total time : 0.005 s
% 0.26/0.27 % Maximum resident set size: 3648 pages
% 0.26/0.27
% 0.26/0.27 % -------------------------------------------------
% 0.26/0.27 % User time : 0.006 s
% 0.26/0.27 % System time : 0.005 s
% 0.26/0.27 % Total time : 0.011 s
% 0.26/0.27 % Maximum resident set size: 4864 pages
% 0.26/0.27 % E exiting
%------------------------------------------------------------------------------