%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP107^1 : TPTP v9.3.1. Released v7.5.0.
% 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 08:04:23 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 239 ( 5 ~; 0 |; 0 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 6 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
partia1833973666xt_a_b: $tType ).
thf(decl_sort2,type,
set_a: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_sort4,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort5,type,
partia1993116613t_unit: $tType ).
thf(decl_sort6,type,
partia539144763t_unit: $tType ).
thf(decl_42,type,
mult_s977248631t_unit: partia539144763t_unit > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(decl_44,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(decl_51,type,
locali1170246543t_unit: partia1993116613t_unit > a > a > set_Product_prod_a_a ).
thf(decl_53,type,
locali1944243560ac_a_b: partia1833973666xt_a_b > set_a > partia539144763t_unit ).
thf(decl_88,type,
r: partia1833973666xt_a_b ).
thf(decl_89,type,
s: set_a ).
thf(decl_90,type,
r2: a ).
thf(decl_91,type,
r3: a ).
thf(decl_92,type,
rel: partia1993116613t_unit ).
thf(decl_93,type,
s2: a ).
thf(decl_94,type,
s3: a ).
thf(conj_0,conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dqMMvKSjN3/E---3.1_1758479.p',conj_0) ).
thf(fact_3_f1,axiom,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dqMMvKSjN3/E---3.1_1758479.p',fact_3_f1) ).
thf(fact_4_f2,axiom,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dqMMvKSjN3/E---3.1_1758479.p',fact_4_f2) ).
thf(fact_0_f3,axiom,
( ( mult_a_ring_ext_a_b @ r @ r2 @ r3 )
= ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) ),
file('/export/starexec/sandbox/tmp/tmp.dqMMvKSjN3/E---3.1_1758479.p',fact_0_f3) ).
thf(fact_1_f4,axiom,
( ( mult_a_ring_ext_a_b @ r @ s2 @ s3 )
= ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ),
file('/export/starexec/sandbox/tmp/tmp.dqMMvKSjN3/E---3.1_1758479.p',fact_1_f4) ).
thf(c_0_5,negated_conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
!= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
!= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
!= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
!= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,plain,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ),
inference(split_conjunct,[status(thm)],[fact_3_f1]) ).
thf(c_0_10,plain,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ),
inference(split_conjunct,[status(thm)],[fact_4_f2]) ).
thf(c_0_11,plain,
( ( mult_a_ring_ext_a_b @ r @ r2 @ r3 )
= ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) ),
inference(split_conjunct,[status(thm)],[fact_0_f3]) ).
thf(c_0_12,plain,
( ( mult_a_ring_ext_a_b @ r @ s2 @ s3 )
= ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ),
inference(split_conjunct,[status(thm)],[fact_1_f4]) ).
thf(c_0_13,negated_conjecture,
( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
!= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP107^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.18 % Computer : n004.cluster.edu
% 0.05/0.18 % Model : x86_64 x86_64
% 0.05/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.18 % Memory : 8046.5625MB
% 0.05/0.18 % OS : Linux 6.8.0-71-generic
% 0.05/0.19 % CPULimit : 300
% 0.05/0.19 % WCLimit : 300
% 0.05/0.19 % DateTime : Tue Sep 29 19:54:22 UTC 2026
% 0.05/0.19 % CPUTime :
% 0.05/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.23 Running higher-order theorem proving
% 0.05/0.26 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.dqMMvKSjN3/E---3.1_1758479.p
% 0.22/0.34 % Version: 3.5.1-ho
% 0.22/0.34 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.22/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting new_ho_3 with 1500s (5) cores
% 0.22/0.34 % Starting pre_casc_2 with 300s (1) cores
% 0.22/0.34 % Starting additional_ho_7 with 300s (1) cores
% 0.22/0.34 % Starting lpo8_s with 300s (1) cores
% 0.22/0.34 % new_ho_3 with pid 1758492 completed with status 0
% 0.22/0.34 % Result found by new_ho_3
% 0.22/0.34 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.22/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting new_ho_3 with 1500s (5) cores
% 0.22/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.22/0.34 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.22/0.34 % Search class: HGHSM-FMLM31-MSFFFFBN
% 0.22/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.34 % Starting new_ho_3 with 151s (1) cores
% 0.22/0.34 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.34 % Starting new_bool_2 with 136s (1) cores
% 0.22/0.34 % Starting new_bool_9 with 136s (1) cores
% 0.22/0.34 % new_ho_3 with pid 1758497 completed with status 0
% 0.22/0.34 % Result found by new_ho_3
% 0.22/0.34 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.22/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting new_ho_3 with 1500s (5) cores
% 0.22/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.22/0.34 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.22/0.34 % Search class: HGHSM-FMLM31-MSFFFFBN
% 0.22/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.34 % Starting new_ho_3 with 151s (1) cores
% 0.22/0.34 % Preprocessing time : 0.010 s
% 0.22/0.34 % Presaturation interreduction done
% 0.22/0.34
% 0.22/0.34 % Proof found!
% 0.22/0.34 % SZS status Theorem
% 0.22/0.34 % SZS output start CNFRefutation
% See solution above
% 0.22/0.34 % Parsed axioms : 440
% 0.22/0.34 % Removed by relevancy pruning/SinE : 109
% 0.22/0.34 % Initial clauses : 949
% 0.22/0.34 % Removed in clause preprocessing : 27
% 0.22/0.34 % Initial clauses in saturation : 922
% 0.22/0.34 % Processed clauses : 46
% 0.22/0.34 % ...of these trivial : 0
% 0.22/0.34 % ...subsumed : 7
% 0.22/0.34 % ...remaining for further processing : 38
% 0.22/0.34 % Other redundant clauses eliminated : 3
% 0.22/0.34 % Clauses deleted for lack of memory : 0
% 0.22/0.34 % Backward-subsumed : 0
% 0.22/0.34 % Backward-rewritten : 1
% 0.22/0.34 % Generated clauses : 3
% 0.22/0.34 % ...of the previous two non-redundant : 4
% 0.22/0.34 % ...aggressively subsumed : 0
% 0.22/0.34 % Contextual simplify-reflections : 0
% 0.22/0.34 % Paramodulations : 0
% 0.22/0.34 % Factorizations : 0
% 0.22/0.34 % NegExts : 0
% 0.22/0.34 % Equation resolutions : 3
% 0.22/0.34 % Disequality decompositions : 0
% 0.22/0.34 % Total rewrite steps : 3
% 0.22/0.34 % ...of those cached : 0
% 0.22/0.34 % Propositional unsat checks : 0
% 0.22/0.34 % Propositional check models : 0
% 0.22/0.34 % Propositional check unsatisfiable : 0
% 0.22/0.34 % Propositional clauses : 0
% 0.22/0.34 % Propositional clauses after purity: 0
% 0.22/0.34 % Propositional unsat core size : 0
% 0.22/0.34 % Propositional preprocessing time : 0.000
% 0.22/0.34 % Propositional encoding time : 0.000
% 0.22/0.34 % Propositional solver time : 0.000
% 0.22/0.34 % Success case prop preproc time : 0.000
% 0.22/0.34 % Success case prop encoding time : 0.000
% 0.22/0.34 % Success case prop solver time : 0.000
% 0.22/0.34 % Current number of processed clauses : 34
% 0.22/0.34 % Positive orientable unit clauses : 22
% 0.22/0.34 % Positive unorientable unit clauses: 0
% 0.22/0.34 % Negative unit clauses : 8
% 0.22/0.34 % Non-unit-clauses : 4
% 0.22/0.34 % Current number of unprocessed clauses: 880
% 0.22/0.34 % ...number of literals in the above : 3968
% 0.22/0.34 % Current number of archived formulas : 0
% 0.22/0.34 % Current number of archived clauses : 1
% 0.22/0.34 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.34 % Non-unit clause-clause subsumptions : 0
% 0.22/0.34 % Unit Clause-clause subsumption calls : 7
% 0.22/0.34 % Rewrite failures with RHS unbound : 0
% 0.22/0.34 % BW rewrite match attempts : 3
% 0.22/0.34 % BW rewrite match successes : 1
% 0.22/0.34 % Condensation attempts : 46
% 0.22/0.34 % Condensation successes : 0
% 0.22/0.34 % Termbank termtop insertions : 73332
% 0.22/0.34 % Search garbage collected termcells : 15812
% 0.22/0.34
% 0.22/0.34 % -------------------------------------------------
% 0.22/0.34 % User time : 0.039 s
% 0.22/0.34 % System time : 0.009 s
% 0.22/0.34 % Total time : 0.048 s
% 0.22/0.34 % Maximum resident set size: 7508 pages
% 0.22/0.34
% 0.22/0.34 % -------------------------------------------------
% 0.22/0.34 % User time : 0.084 s
% 0.22/0.34 % System time : 0.033 s
% 0.22/0.34 % Total time : 0.117 s
% 0.22/0.34 % Maximum resident set size: 5632 pages
% 0.22/0.34 % E exiting
%------------------------------------------------------------------------------