%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP106^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:04:22 AM UTC 2026
% Result : Theorem 0.99s 0.51s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 419 ( 10 ~; 5 |; 0 &; 402 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
partia1993116613t_unit: $tType ).
thf(decl_sort2,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort3,type,
partia1833973666xt_a_b: $tType ).
thf(decl_sort4,type,
a: $tType ).
thf(decl_sort5,type,
product_prod_a_a: $tType ).
thf(decl_23,type,
partia206007992t_unit: partia1993116613t_unit > set_Product_prod_a_a ).
thf(decl_33,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(decl_46,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(decl_53,type,
add_a_b: partia1833973666xt_a_b > a > a > a ).
thf(decl_59,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(decl_61,type,
r: partia1833973666xt_a_b ).
thf(decl_62,type,
r2: a ).
thf(decl_63,type,
r3: a ).
thf(decl_64,type,
r4: a ).
thf(decl_65,type,
rel: partia1993116613t_unit ).
thf(decl_66,type,
s: a ).
thf(decl_67,type,
s2: a ).
thf(decl_68,type,
s3: a ).
thf(conj_0,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ),
file('/export/starexec/sandbox2/tmp/tmp.cpxdRsMsd3/E---3.1_562936.p',conj_0) ).
thf(fact_4_closed__rel__add,axiom,
! [X4: a,X5: a,X6: a,X7: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X5 ) @ ( partia206007992t_unit @ rel ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X6 @ X7 ) @ ( partia206007992t_unit @ rel ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X7 @ X4 ) @ ( mult_a_ring_ext_a_b @ r @ X5 @ X6 ) ) @ ( mult_a_ring_ext_a_b @ r @ X5 @ X7 ) ) @ ( partia206007992t_unit @ rel ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cpxdRsMsd3/E---3.1_562936.p',fact_4_closed__rel__add) ).
thf(fact_10_f5,axiom,
member449909584od_a_a @ ( product_Pair_a_a @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( partia206007992t_unit @ rel ),
file('/export/starexec/sandbox2/tmp/tmp.cpxdRsMsd3/E---3.1_562936.p',fact_10_f5) ).
thf(fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ s ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cpxdRsMsd3/E---3.1_562936.p',fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062) ).
thf(fact_11_f4,axiom,
member449909584od_a_a @ ( product_Pair_a_a @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) ) @ ( partia206007992t_unit @ rel ),
file('/export/starexec/sandbox2/tmp/tmp.cpxdRsMsd3/E---3.1_562936.p',fact_11_f4) ).
thf(c_0_5,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X858: a,X859: a,X860: a,X861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X858 @ X859 ) @ ( partia206007992t_unit @ rel ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X860 @ X861 ) @ ( partia206007992t_unit @ rel ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X861 @ X858 ) @ ( mult_a_ring_ext_a_b @ r @ X859 @ X860 ) ) @ ( mult_a_ring_ext_a_b @ r @ X859 @ X861 ) ) @ ( partia206007992t_unit @ rel ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_closed__rel__add])])]) ).
thf(c_0_8,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: a,X2: a,X3: a,X4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X4 @ X1 ) @ ( mult_a_ring_ext_a_b @ r @ X2 @ X3 ) ) @ ( mult_a_ring_ext_a_b @ r @ X2 @ X4 ) ) @ ( partia206007992t_unit @ rel ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ ( partia206007992t_unit @ rel ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ X4 ) @ ( partia206007992t_unit @ rel ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
member449909584od_a_a @ ( product_Pair_a_a @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( partia206007992t_unit @ rel ),
inference(split_conjunct,[status(thm)],[fact_10_f5]) ).
thf(c_0_11,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ s ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ),
inference(split_conjunct,[status(thm)],[fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062]) ).
thf(c_0_13,plain,
! [X1: a,X2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ X1 ) @ ( mult_a_ring_ext_a_b @ r @ X2 @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ X2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ ( partia206007992t_unit @ rel ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
member449909584od_a_a @ ( product_Pair_a_a @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) ) @ ( partia206007992t_unit @ rel ),
inference(split_conjunct,[status(thm)],[fact_11_f4]) ).
thf(c_0_15,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ r2 @ r4 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ s ) @ ( mult_a_ring_ext_a_b @ r @ r3 @ r4 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) @ ( partia206007992t_unit @ rel ) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP106^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:55:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.22/0.28 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.cpxdRsMsd3/E---3.1_562936.p
% 0.99/0.51 % Version: 3.5.1-ho
% 0.99/0.51 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.99/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.51 % Starting new_ho_3 with 1500s (5) cores
% 0.99/0.51 % Starting pre_casc_2 with 300s (1) cores
% 0.99/0.51 % Starting additional_ho_7 with 300s (1) cores
% 0.99/0.51 % Starting lpo8_s with 300s (1) cores
% 0.99/0.51 % new_ho_3 with pid 562983 completed with status 0
% 0.99/0.51 % Result found by new_ho_3
% 0.99/0.51 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.99/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.51 % Starting new_ho_3 with 1500s (5) cores
% 0.99/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.99/0.51 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.99/0.51 % Search class: HGUSM-FSLM31-DSFFFFBN
% 0.99/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.99/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.99/0.51 % Starting new_ho_3 with 151s (1) cores
% 0.99/0.51 % Starting sh5l with 136s (1) cores
% 0.99/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.99/0.51 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.99/0.51 % new_bool_1 with pid 562994 completed with status 0
% 0.99/0.51 % Result found by new_bool_1
% 0.99/0.51 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.99/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.51 % Starting new_ho_3 with 1500s (5) cores
% 0.99/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.99/0.51 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.99/0.51 % Search class: HGUSM-FSLM31-DSFFFFBN
% 0.99/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.99/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.99/0.51 % Starting new_ho_3 with 151s (1) cores
% 0.99/0.51 % Starting sh5l with 136s (1) cores
% 0.99/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.99/0.51 % Preprocessing time : 0.007 s
% 0.99/0.51 % Presaturation interreduction done
% 0.99/0.51
% 0.99/0.51 % Proof found!
% 0.99/0.51 % SZS status Theorem
% 0.99/0.51 % SZS output start CNFRefutation
% See solution above
% 0.99/0.51 % Parsed axioms : 339
% 0.99/0.51 % Removed by relevancy pruning/SinE : 89
% 0.99/0.51 % Initial clauses : 488
% 0.99/0.51 % Removed in clause preprocessing : 18
% 0.99/0.51 % Initial clauses in saturation : 470
% 0.99/0.51 % Processed clauses : 2095
% 0.99/0.51 % ...of these trivial : 62
% 0.99/0.51 % ...subsumed : 815
% 0.99/0.51 % ...remaining for further processing : 1218
% 0.99/0.51 % Other redundant clauses eliminated : 86
% 0.99/0.51 % Clauses deleted for lack of memory : 0
% 0.99/0.51 % Backward-subsumed : 7
% 0.99/0.51 % Backward-rewritten : 89
% 0.99/0.51 % Generated clauses : 5357
% 0.99/0.51 % ...of the previous two non-redundant : 4581
% 0.99/0.51 % ...aggressively subsumed : 0
% 0.99/0.51 % Contextual simplify-reflections : 11
% 0.99/0.51 % Paramodulations : 5177
% 0.99/0.51 % Factorizations : 2
% 0.99/0.51 % NegExts : 3
% 0.99/0.51 % Equation resolutions : 102
% 0.99/0.51 % Disequality decompositions : 0
% 0.99/0.51 % Total rewrite steps : 4305
% 0.99/0.51 % ...of those cached : 3530
% 0.99/0.51 % Propositional unsat checks : 0
% 0.99/0.51 % Propositional check models : 0
% 0.99/0.51 % Propositional check unsatisfiable : 0
% 0.99/0.51 % Propositional clauses : 0
% 0.99/0.51 % Propositional clauses after purity: 0
% 0.99/0.51 % Propositional unsat core size : 0
% 0.99/0.51 % Propositional preprocessing time : 0.000
% 0.99/0.51 % Propositional encoding time : 0.000
% 0.99/0.51 % Propositional solver time : 0.000
% 0.99/0.51 % Success case prop preproc time : 0.000
% 0.99/0.51 % Success case prop encoding time : 0.000
% 0.99/0.51 % Success case prop solver time : 0.000
% 0.99/0.51 % Current number of processed clauses : 690
% 0.99/0.51 % Positive orientable unit clauses : 304
% 0.99/0.51 % Positive unorientable unit clauses: 8
% 0.99/0.51 % Negative unit clauses : 71
% 0.99/0.51 % Non-unit-clauses : 307
% 0.99/0.51 % Current number of unprocessed clauses: 3117
% 0.99/0.51 % ...number of literals in the above : 6918
% 0.99/0.51 % Current number of archived formulas : 0
% 0.99/0.51 % Current number of archived clauses : 494
% 0.99/0.51 % Clause-clause subsumption calls (NU) : 87698
% 0.99/0.51 % Rec. Clause-clause subsumption calls : 20988
% 0.99/0.51 % Non-unit clause-clause subsumptions : 205
% 0.99/0.51 % Unit Clause-clause subsumption calls : 6165
% 0.99/0.51 % Rewrite failures with RHS unbound : 30
% 0.99/0.51 % BW rewrite match attempts : 12435
% 0.99/0.51 % BW rewrite match successes : 116
% 0.99/0.51 % Condensation attempts : 0
% 0.99/0.51 % Condensation successes : 0
% 0.99/0.51 % Termbank termtop insertions : 276649
% 0.99/0.51 % Search garbage collected termcells : 7962
% 0.99/0.51
% 0.99/0.51 % -------------------------------------------------
% 0.99/0.51 % User time : 0.184 s
% 0.99/0.51 % System time : 0.014 s
% 0.99/0.51 % Total time : 0.198 s
% 0.99/0.51 % Maximum resident set size: 5992 pages
% 0.99/0.51
% 0.99/0.51 % -------------------------------------------------
% 0.99/0.51 % User time : 0.901 s
% 0.99/0.51 % System time : 0.048 s
% 0.99/0.51 % Total time : 0.948 s
% 0.99/0.51 % Maximum resident set size: 5376 pages
% 0.99/0.51 % E exiting
%------------------------------------------------------------------------------