%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP150^1 : 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 : n026.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 08:04:31 AM UTC 2026
% Result : Theorem 0.48s 0.43s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 179 ( 8 ~; 3 |; 1 &; 166 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 ^; 32 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_sort2,type,
polyno727731844poly_a: $tType ).
thf(decl_sort3,type,
list_a: $tType ).
thf(decl_28,type,
times_times_a: a > a > a ).
thf(decl_34,type,
polyno422358502poly_a: list_a > polyno727731844poly_a > a ).
thf(decl_60,type,
polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(decl_72,type,
polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(decl_85,type,
p: polyno727731844poly_a ).
thf(decl_86,type,
q: polyno727731844poly_a ).
thf(decl_87,type,
esk1_0: list_a ).
thf(conj_0,conjecture,
( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.PYw5ZuNzrm/E---3.1_1109909.p',conj_0) ).
thf(fact_10_polymul,axiom,
! [X18: list_a,X2: polyno727731844poly_a,X3: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X18 @ ( polyno1934269411ymul_a @ X2 @ X3 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X18 @ X2 ) @ ( polyno422358502poly_a @ X18 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PYw5ZuNzrm/E---3.1_1109909.p',fact_10_polymul) ).
thf(fact_29_Ipoly_Osimps_I6_J,axiom,
! [X72: list_a,X73: polyno727731844poly_a,X74: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X72 @ ( polyno1491482291_Mul_a @ X73 @ X74 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X72 @ X73 ) @ ( polyno422358502poly_a @ X72 @ X74 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PYw5ZuNzrm/E---3.1_1109909.p',fact_29_Ipoly_Osimps_I6_J) ).
thf(fact_132_mult_Ocommute,axiom,
( times_times_a
= ( ^ [X228: a,X229: a] : ( times_times_a @ X229 @ X228 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PYw5ZuNzrm/E---3.1_1109909.p',fact_132_mult_Ocommute) ).
thf(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062,axiom,
( ! [X1: list_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ X1 @ ( polyno1934269411ymul_a @ q @ p ) ) )
<=> ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PYw5ZuNzrm/E---3.1_1109909.p',fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062) ).
thf(c_0_5,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,plain,
! [X1517: list_a,X1518: polyno727731844poly_a,X1519: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1517 @ ( polyno1934269411ymul_a @ X1518 @ X1519 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X1517 @ X1518 ) @ ( polyno422358502poly_a @ X1517 @ X1519 ) ) ),
inference(variable_rename,[status(thm)],[fact_10_polymul]) ).
thf(c_0_7,plain,
! [X1586: list_a,X1587: polyno727731844poly_a,X1588: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1586 @ ( polyno1491482291_Mul_a @ X1587 @ X1588 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X1586 @ X1587 ) @ ( polyno422358502poly_a @ X1586 @ X1588 ) ) ),
inference(variable_rename,[status(thm)],[fact_29_Ipoly_Osimps_I6_J]) ).
thf(c_0_8,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X1454: a,X1455: a] :
( ( times_times_a @ X1454 @ X1455 )
= ( times_times_a @ X1455 @ X1454 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_132_mult_Ocommute])]) ).
thf(c_0_10,plain,
! [X1496: list_a] :
( ( ( ( polyno422358502poly_a @ esk1_0 @ ( polyno1934269411ymul_a @ p @ q ) )
!= ( polyno422358502poly_a @ esk1_0 @ ( polyno1934269411ymul_a @ q @ p ) ) )
| ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) )
& ( ( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) )
| ( ( polyno422358502poly_a @ X1496 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ X1496 @ ( polyno1934269411ymul_a @ q @ p ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062])])])])]) ).
thf(c_0_11,plain,
! [X1: list_a,X2: polyno727731844poly_a,X3: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1934269411ymul_a @ X2 @ X3 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X1 @ X2 ) @ ( polyno422358502poly_a @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,plain,
! [X1: list_a,X2: polyno727731844poly_a,X3: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1491482291_Mul_a @ X2 @ X3 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X1 @ X2 ) @ ( polyno422358502poly_a @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X1865: a,X1866: a] :
( ( times_times_a @ X1865 @ X1866 )
= ( times_times_a @ X1866 @ X1865 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
( ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) )
| ( ( polyno422358502poly_a @ esk1_0 @ ( polyno1934269411ymul_a @ p @ q ) )
!= ( polyno422358502poly_a @ esk1_0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X1: list_a,X2: polyno727731844poly_a,X3: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1934269411ymul_a @ X2 @ X3 ) )
= ( polyno422358502poly_a @ X1 @ ( polyno1491482291_Mul_a @ X2 @ X3 ) ) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
! [X22: a,X21: a] :
( ( times_times_a @ X21 @ X22 )
= ( times_times_a @ X22 @ X21 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
( ( polyno422358502poly_a @ esk1_0 @ ( polyno1491482291_Mul_a @ q @ p ) )
!= ( polyno422358502poly_a @ esk1_0 @ ( polyno1491482291_Mul_a @ p @ q ) ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_17]) ).
thf(c_0_20,plain,
! [X1: list_a,X3: polyno727731844poly_a,X2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1491482291_Mul_a @ X2 @ X3 ) )
= ( polyno422358502poly_a @ X1 @ ( polyno1491482291_Mul_a @ X3 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_12]) ).
thf(c_0_21,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP150^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:04:54 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.18/0.29 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.PYw5ZuNzrm/E---3.1_1109909.p
% 0.48/0.43 % Version: 3.5.1-ho
% 0.48/0.43 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.48/0.43 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.43 % Starting new_ho_10 with 900s (3) cores
% 0.48/0.43 % Starting sh2lt with 300s (1) cores
% 0.48/0.43 % Starting new_ho_5 with 300s (1) cores
% 0.48/0.43 % Starting full_lambda_5 with 300s (1) cores
% 0.48/0.43 % Starting sh9 with 300s (1) cores
% 0.48/0.43 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.48/0.43 % sh9 with pid 1109926 completed with status 0
% 0.48/0.43 % Result found by sh9
% 0.48/0.43 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.48/0.43 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.43 % Starting new_ho_10 with 900s (3) cores
% 0.48/0.43 % Starting sh2lt with 300s (1) cores
% 0.48/0.43 % Starting new_ho_5 with 300s (1) cores
% 0.48/0.43 % Starting full_lambda_5 with 300s (1) cores
% 0.48/0.43 % Starting sh9 with 300s (1) cores
% 0.48/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.48/0.43 % No SInE strategy applied
% 0.48/0.43 % Search class: HGUSM-SMLS31-MSFFFMBN
% 0.48/0.43 % partial match(2): HGHSM-SMLM31-MSFFFMBN
% 0.48/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.48/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.48/0.43 % SubtermCWHack with pid 1109930 completed with status 0
% 0.48/0.43 % Result found by SubtermCWHack
% 0.48/0.43 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.48/0.43 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.43 % Starting new_ho_10 with 900s (3) cores
% 0.48/0.43 % Starting sh2lt with 300s (1) cores
% 0.48/0.43 % Starting new_ho_5 with 300s (1) cores
% 0.48/0.43 % Starting full_lambda_5 with 300s (1) cores
% 0.48/0.43 % Starting sh9 with 300s (1) cores
% 0.48/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.48/0.43 % No SInE strategy applied
% 0.48/0.43 % Search class: HGUSM-SMLS31-MSFFFMBN
% 0.48/0.43 % partial match(2): HGHSM-SMLM31-MSFFFMBN
% 0.48/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.48/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.48/0.43 % Preprocessing time : 0.010 s
% 0.48/0.43
% 0.48/0.43 % Proof found!
% 0.48/0.43 % SZS status Theorem
% 0.48/0.43 % SZS output start CNFRefutation
% See solution above
% 0.48/0.43 % Parsed axioms : 426
% 0.48/0.43 % Removed by relevancy pruning/SinE : 0
% 0.48/0.43 % Initial clauses : 1313
% 0.48/0.43 % Removed in clause preprocessing : 122
% 0.48/0.43 % Initial clauses in saturation : 1191
% 0.48/0.43 % Processed clauses : 982
% 0.48/0.43 % ...of these trivial : 54
% 0.48/0.43 % ...subsumed : 367
% 0.48/0.43 % ...remaining for further processing : 561
% 0.48/0.43 % Other redundant clauses eliminated : 58
% 0.48/0.43 % Clauses deleted for lack of memory : 0
% 0.48/0.43 % Backward-subsumed : 3
% 0.48/0.43 % Backward-rewritten : 21
% 0.48/0.43 % Generated clauses : 2714
% 0.48/0.43 % ...of the previous two non-redundant : 1959
% 0.48/0.43 % ...aggressively subsumed : 0
% 0.48/0.43 % Contextual simplify-reflections : 1
% 0.48/0.43 % Paramodulations : 2638
% 0.48/0.43 % Factorizations : 0
% 0.48/0.43 % NegExts : 0
% 0.48/0.43 % Equation resolutions : 77
% 0.48/0.43 % Disequality decompositions : 0
% 0.48/0.43 % Total rewrite steps : 1632
% 0.48/0.43 % ...of those cached : 1250
% 0.48/0.43 % Propositional unsat checks : 0
% 0.48/0.43 % Propositional check models : 0
% 0.48/0.43 % Propositional check unsatisfiable : 0
% 0.48/0.43 % Propositional clauses : 0
% 0.48/0.43 % Propositional clauses after purity: 0
% 0.48/0.43 % Propositional unsat core size : 0
% 0.48/0.43 % Propositional preprocessing time : 0.000
% 0.48/0.43 % Propositional encoding time : 0.000
% 0.48/0.43 % Propositional solver time : 0.000
% 0.48/0.43 % Success case prop preproc time : 0.000
% 0.48/0.43 % Success case prop encoding time : 0.000
% 0.48/0.43 % Success case prop solver time : 0.000
% 0.48/0.43 % Current number of processed clauses : 488
% 0.48/0.43 % Positive orientable unit clauses : 262
% 0.48/0.43 % Positive unorientable unit clauses: 15
% 0.48/0.43 % Negative unit clauses : 82
% 0.48/0.43 % Non-unit-clauses : 129
% 0.48/0.43 % Current number of unprocessed clauses: 2166
% 0.48/0.43 % ...number of literals in the above : 9822
% 0.48/0.43 % Current number of archived formulas : 0
% 0.48/0.43 % Current number of archived clauses : 24
% 0.48/0.43 % Clause-clause subsumption calls (NU) : 8825
% 0.48/0.43 % Rec. Clause-clause subsumption calls : 7785
% 0.48/0.43 % Non-unit clause-clause subsumptions : 235
% 0.48/0.43 % Unit Clause-clause subsumption calls : 3765
% 0.48/0.43 % Rewrite failures with RHS unbound : 0
% 0.48/0.43 % BW rewrite match attempts : 918
% 0.48/0.43 % BW rewrite match successes : 102
% 0.48/0.43 % Condensation attempts : 0
% 0.48/0.43 % Condensation successes : 0
% 0.48/0.43 % Termbank termtop insertions : 104922
% 0.48/0.43 % Search garbage collected termcells : 11796
% 0.48/0.43
% 0.48/0.43 % -------------------------------------------------
% 0.48/0.43 % User time : 0.089 s
% 0.48/0.43 % System time : 0.010 s
% 0.48/0.43 % Total time : 0.099 s
% 0.48/0.43 % Maximum resident set size: 7436 pages
% 0.48/0.43
% 0.48/0.43 % -------------------------------------------------
% 0.48/0.43 % User time : 0.105 s
% 0.48/0.43 % System time : 0.014 s
% 0.48/0.43 % Total time : 0.119 s
% 0.48/0.43 % Maximum resident set size: 5632 pages
% 0.48/0.43 % E exiting
%------------------------------------------------------------------------------