%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP156^1 : 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 : n014.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 08:04:32 AM UTC 2026
% Result : Theorem 0.37s 0.40s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 201 ( 15 ~; 9 |; 3 &; 170 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_sort3,type,
product_prod_a_a: $tType ).
thf(decl_sort4,type,
set_Product_prod_a_a: $tType ).
thf(decl_23,type,
one_one_real: real ).
thf(decl_34,type,
plus_plus_real: real > real > real ).
thf(decl_43,type,
plus_plus_a: a > a > a ).
thf(decl_54,type,
zero_zero_real: real ).
thf(decl_58,type,
zero_zero_a: a ).
thf(decl_88,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(decl_99,type,
real_V1035702895aleR_a: real > a > a ).
thf(decl_108,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(decl_114,type,
relation: set_Product_prod_a_a ).
thf(decl_115,type,
u: real ).
thf(decl_116,type,
v: real ).
thf(decl_117,type,
x: a ).
thf(decl_118,type,
y: a ).
thf(conj_0,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation,
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',conj_0) ).
thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,axiom,
( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062) ).
thf(fact_7_u__0,axiom,
( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_7_u__0) ).
thf(fact_72_add__cancel__right__right,axiom,
! [X166: real,X167: real] :
( ( X166
= ( plus_plus_real @ X166 @ X167 ) )
<=> ( X167 = zero_zero_real ) ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_72_add__cancel__right__right) ).
thf(fact_9_assms_I5_J,axiom,
( ( plus_plus_real @ u @ v )
= one_one_real ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_9_assms_I5_J) ).
thf(fact_241_scaleR__one,axiom,
! [X1: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X1 )
= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_241_scaleR__one) ).
thf(fact_238_scale__zero__left,axiom,
! [X1: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X1 )
= zero_zero_a ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_238_scale__zero__left) ).
thf(fact_96_add_Oright__neutral,axiom,
! [X5: a] :
( ( plus_plus_a @ X5 @ zero_zero_a )
= X5 ),
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_96_add_Oright__neutral) ).
thf(fact_5_assms_I2_J,axiom,
member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation,
file('/export/starexec/sandbox2/tmp/tmp.OxFVXhCqFr/E---3.1_3143372.p',fact_5_assms_I2_J) ).
thf(c_0_9,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_10,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
thf(c_0_11,plain,
( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(fof_simplification,[status(thm)],[fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062]) ).
thf(c_0_12,plain,
( ( u != zero_zero_real )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_u__0])]) ).
thf(c_0_13,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
( ( u = zero_zero_real )
| ( u = one_one_real )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
| ( u != zero_zero_real ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
( ( u = zero_zero_real )
| ( u = one_one_real )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
u != zero_zero_real,
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
! [X1802: real,X1803: real] :
( ( ( X1802
!= ( plus_plus_real @ X1802 @ X1803 ) )
| ( X1803 = zero_zero_real ) )
& ( ( X1803 != zero_zero_real )
| ( X1802
= ( plus_plus_real @ X1802 @ X1803 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_add__cancel__right__right])])]) ).
thf(c_0_20,plain,
( ( plus_plus_real @ u @ v )
= one_one_real ),
inference(split_conjunct,[status(thm)],[fact_9_assms_I5_J]) ).
thf(c_0_21,plain,
u = one_one_real,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
thf(c_0_22,plain,
! [X4: real,X7: real] :
( ( X7 = zero_zero_real )
| ( X4
!= ( plus_plus_real @ X4 @ X7 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
( ( plus_plus_real @ one_one_real @ v )
= one_one_real ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,plain,
! [X1576: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X1576 )
= X1576 ),
inference(variable_rename,[status(thm)],[fact_241_scaleR__one]) ).
thf(c_0_25,plain,
! [X1573: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X1573 )
= zero_zero_a ),
inference(variable_rename,[status(thm)],[fact_238_scale__zero__left]) ).
thf(c_0_26,plain,
! [X1521: a] :
( ( plus_plus_a @ X1521 @ zero_zero_a )
= X1521 ),
inference(variable_rename,[status(thm)],[fact_96_add_Oright__neutral]) ).
thf(c_0_27,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ one_one_real @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ),
inference(rw,[status(thm)],[c_0_16,c_0_21]) ).
thf(c_0_28,plain,
v = zero_zero_real,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_29,plain,
! [X1: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,plain,
! [X1: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X1 )
= zero_zero_a ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_31,plain,
! [X1: a] :
( ( plus_plus_a @ X1 @ zero_zero_a )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_32,plain,
member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation,
inference(split_conjunct,[status(thm)],[fact_5_assms_I2_J]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP156^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 20:02:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.30 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.OxFVXhCqFr/E---3.1_3143372.p
% 0.37/0.39 % Version: 3.5.1-ho
% 0.37/0.39 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.37/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.39 % Starting new_ho_3 with 1500s (5) cores
% 0.37/0.39 % Starting pre_casc_2 with 300s (1) cores
% 0.37/0.39 % Starting additional_ho_7 with 300s (1) cores
% 0.37/0.39 % Starting lpo8_s with 300s (1) cores
% 0.37/0.39 % new_ho_3 with pid 3143424 completed with status 0
% 0.37/0.39 % Result found by new_ho_3
% 0.37/0.39 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.37/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.39 % Starting new_ho_3 with 1500s (5) cores
% 0.37/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.37/0.39 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.37/0.39 % Search class: HGUSM-FSLM31-MSFFFFBN
% 0.37/0.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.39 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.39 % Starting new_ho_3 with 151s (1) cores
% 0.37/0.39 % Starting sh5l with 226s (1) cores
% 0.37/0.39 % Starting new_bool_1 with 226s (1) cores
% 0.37/0.39 % Starting new_bool_2 with 226s (1) cores
% 0.37/0.39 % new_ho_3 with pid 3143436 completed with status 0
% 0.37/0.40 % Result found by new_ho_3
% 0.37/0.40 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.37/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.40 % Starting new_ho_3 with 1500s (5) cores
% 0.37/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.37/0.40 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.37/0.40 % Search class: HGUSM-FSLM31-MSFFFFBN
% 0.37/0.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.40 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.40 % Starting new_ho_3 with 151s (1) cores
% 0.37/0.40 % Preprocessing time : 0.007 s
% 0.37/0.40 % Presaturation interreduction done
% 0.37/0.40
% 0.37/0.40 % Proof found!
% 0.37/0.40 % SZS status Theorem
% 0.37/0.40 % SZS output start CNFRefutation
% See solution above
% 0.37/0.40 % Parsed axioms : 482
% 0.37/0.40 % Removed by relevancy pruning/SinE : 226
% 0.37/0.40 % Initial clauses : 453
% 0.37/0.40 % Removed in clause preprocessing : 35
% 0.37/0.40 % Initial clauses in saturation : 418
% 0.37/0.40 % Processed clauses : 476
% 0.37/0.40 % ...of these trivial : 33
% 0.37/0.40 % ...subsumed : 132
% 0.37/0.40 % ...remaining for further processing : 311
% 0.37/0.40 % Other redundant clauses eliminated : 50
% 0.37/0.40 % Clauses deleted for lack of memory : 0
% 0.37/0.40 % Backward-subsumed : 1
% 0.37/0.40 % Backward-rewritten : 6
% 0.37/0.40 % Generated clauses : 61
% 0.37/0.40 % ...of the previous two non-redundant : 19
% 0.37/0.40 % ...aggressively subsumed : 0
% 0.37/0.40 % Contextual simplify-reflections : 0
% 0.37/0.40 % Paramodulations : 13
% 0.37/0.40 % Factorizations : 0
% 0.37/0.40 % NegExts : 0
% 0.37/0.40 % Equation resolutions : 50
% 0.37/0.40 % Disequality decompositions : 0
% 0.37/0.40 % Total rewrite steps : 93
% 0.37/0.40 % ...of those cached : 49
% 0.37/0.40 % Propositional unsat checks : 0
% 0.37/0.40 % Propositional check models : 0
% 0.37/0.40 % Propositional check unsatisfiable : 0
% 0.37/0.40 % Propositional clauses : 0
% 0.37/0.40 % Propositional clauses after purity: 0
% 0.37/0.40 % Propositional unsat core size : 0
% 0.37/0.40 % Propositional preprocessing time : 0.000
% 0.37/0.40 % Propositional encoding time : 0.000
% 0.37/0.40 % Propositional solver time : 0.000
% 0.37/0.40 % Success case prop preproc time : 0.000
% 0.37/0.40 % Success case prop encoding time : 0.000
% 0.37/0.40 % Success case prop solver time : 0.000
% 0.37/0.40 % Current number of processed clauses : 40
% 0.37/0.40 % Positive orientable unit clauses : 24
% 0.37/0.40 % Positive unorientable unit clauses: 0
% 0.37/0.40 % Negative unit clauses : 7
% 0.37/0.40 % Non-unit-clauses : 9
% 0.37/0.40 % Current number of unprocessed clauses: 176
% 0.37/0.40 % ...number of literals in the above : 431
% 0.37/0.40 % Current number of archived formulas : 0
% 0.37/0.40 % Current number of archived clauses : 223
% 0.37/0.40 % Clause-clause subsumption calls (NU) : 11372
% 0.37/0.40 % Rec. Clause-clause subsumption calls : 8447
% 0.37/0.40 % Non-unit clause-clause subsumptions : 141
% 0.37/0.40 % Unit Clause-clause subsumption calls : 227
% 0.37/0.40 % Rewrite failures with RHS unbound : 0
% 0.37/0.40 % BW rewrite match attempts : 53
% 0.37/0.40 % BW rewrite match successes : 46
% 0.37/0.40 % Condensation attempts : 476
% 0.37/0.40 % Condensation successes : 12
% 0.37/0.40 % Termbank termtop insertions : 37956
% 0.37/0.40 % Search garbage collected termcells : 8364
% 0.37/0.40
% 0.37/0.40 % -------------------------------------------------
% 0.37/0.40 % User time : 0.053 s
% 0.37/0.40 % System time : 0.012 s
% 0.37/0.40 % Total time : 0.065 s
% 0.37/0.40 % Maximum resident set size: 5864 pages
% 0.37/0.40
% 0.37/0.40 % -------------------------------------------------
% 0.37/0.40 % User time : 0.180 s
% 0.37/0.40 % System time : 0.035 s
% 0.37/0.40 % Total time : 0.216 s
% 0.37/0.40 % Maximum resident set size: 5888 pages
% 0.37/0.40 % E exiting
%------------------------------------------------------------------------------