%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW284+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Thu Sep 24 03:10:13 PM UTC 2026
% Result : Theorem 8.36s 1.73s
% Output : CNFRefutation 8.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 24 unt; 0 def)
% Number of atoms : 68 ( 43 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 54 ( 26 ~; 21 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(conj_0,hypothesis,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_coeff__0,axiom,
! [X15,X5] :
( class_Groups_Ozero(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X15) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(fact_poly__0,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(conj_1,conjecture,
v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_pe,axiom,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_poly__eq__iff,axiom,
! [X7,X6,X5] :
( ( class_Rings_Oidom(X5)
& class_Int_Oring__char__0(X5) )
=> ( c_Polynomial_Opoly(X5,X6) = c_Polynomial_Opoly(X5,X7)
<=> X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(c_0_11,plain,
! [X91,X92] :
( X92 = X91
| hAPP(X92,esk1_2(X91,X92)) != hAPP(X91,esk1_2(X91,X92)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
fof(c_0_12,hypothesis,
! [X3083] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3083) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[conj_0]) ).
fof(c_0_13,plain,
! [X285,X286] :
( hAPP(c_Polynomial_Ocoeff(X286,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X286))),X285) = c_Groups_Ozero__class_Ozero(X286)
| ~ class_Groups_Ozero(X286) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__0])])]) ).
fof(c_0_14,plain,
! [X94,X95] :
( hAPP(c_Polynomial_Opoly(X95,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X95))),X94) = c_Groups_Ozero__class_Ozero(X95)
| ~ class_Rings_Ocomm__semiring__0(X95) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])])]) ).
fof(c_0_15,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_0_16,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ class_Groups_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pe]) ).
cnf(c_0_20,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(c_0_21,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_23,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_24,plain,
! [X98,X99,X100] :
( ( ~ class_Rings_Oidom(X100)
| ~ class_Int_Oring__char__0(X100)
| c_Polynomial_Opoly(X100,X99) = c_Polynomial_Opoly(X100,X98)
| X99 != X98 )
& ( ~ class_Rings_Oidom(X100)
| ~ class_Int_Oring__char__0(X100)
| X99 = X98
| c_Polynomial_Opoly(X100,X99) != c_Polynomial_Opoly(X100,X98) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])])]) ).
cnf(c_0_25,hypothesis,
( hAPP(X1,esk1_2(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,plain,
hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_27,plain,
( ~ class_Groups_Ozero(X2)
| hAPP(X1,esk1_2(c_Polynomial_Ocoeff(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X1)) != c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Polynomial_Ocoeff(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_28,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22])]) ).
fof(c_0_29,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ class_Rings_Oidom(X1)
| ~ class_Int_Oring__char__0(X1)
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q) = c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(c_0_33,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(c_0_34,plain,
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,X1) != c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p)
| v_q = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_19]),c_0_20])]) ).
cnf(c_0_38,negated_conjecture,
v_q != v_p,
inference(rw,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW284+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 09:44:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.36/1.73 % Version: 3.5.1
% 8.36/1.73 % Preprocessing class: FMLMSMSSSSSNFFN.
% 8.36/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.36/1.73 % Starting new_bool_3 with 300s (1) cores
% 8.36/1.73 % Starting new_bool_1 with 300s (1) cores
% 8.36/1.73 % Starting sh5l with 300s (1) cores
% 8.36/1.73 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 476224 completed with status 0
% 8.36/1.73 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 8.36/1.73 % Preprocessing class: FMLMSMSSSSSNFFN.
% 8.36/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.36/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.36/1.73 % No SInE strategy applied
% 8.36/1.73 % Search class: FGHSM-SMLM32-DFFFFFNN
% 8.36/1.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.36/1.73 % Starting SubtermCWHack with 136s (1) cores
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 8.36/1.73 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 8.36/1.73 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 8.36/1.73 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 476246 completed with status 0
% 8.36/1.73 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 8.36/1.73 % Preprocessing class: FMLMSMSSSSSNFFN.
% 8.36/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.36/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.36/1.73 % No SInE strategy applied
% 8.36/1.73 % Search class: FGHSM-SMLM32-DFFFFFNN
% 8.36/1.73 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.36/1.73 % Starting SubtermCWHack with 136s (1) cores
% 8.36/1.73 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 8.36/1.73 % Preprocessing time : 0.026 s
% 8.36/1.73
% 8.36/1.73 % Proof found!
% 8.36/1.73 % SZS status Theorem
% 8.36/1.73 % SZS output start CNFRefutation
% See solution above
% 8.36/1.73 % Parsed axioms : 1181
% 8.36/1.73 % Removed by relevancy pruning/SinE : 0
% 8.36/1.73 % Initial clauses : 1609
% 8.36/1.73 % Removed in clause preprocessing : 75
% 8.36/1.73 % Initial clauses in saturation : 1534
% 8.36/1.73 % Processed clauses : 3566
% 8.36/1.73 % ...of these trivial : 233
% 8.36/1.73 % ...subsumed : 1426
% 8.36/1.73 % ...remaining for further processing : 1907
% 8.36/1.73 % Other redundant clauses eliminated : 256
% 8.36/1.73 % Clauses deleted for lack of memory : 0
% 8.36/1.73 % Backward-subsumed : 18
% 8.36/1.73 % Backward-rewritten : 84
% 8.36/1.73 % Generated clauses : 52695
% 8.36/1.73 % ...of the previous two non-redundant : 47705
% 8.36/1.73 % ...aggressively subsumed : 0
% 8.36/1.73 % Contextual simplify-reflections : 3
% 8.36/1.73 % Paramodulations : 52212
% 8.36/1.73 % Factorizations : 8
% 8.36/1.73 % NegExts : 0
% 8.36/1.73 % Equation resolutions : 475
% 8.36/1.73 % Disequality decompositions : 0
% 8.36/1.73 % Total rewrite steps : 29897
% 8.36/1.73 % ...of those cached : 26875
% 8.36/1.73 % Propositional unsat checks : 0
% 8.36/1.73 % Propositional check models : 0
% 8.36/1.73 % Propositional check unsatisfiable : 0
% 8.36/1.73 % Propositional clauses : 0
% 8.36/1.73 % Propositional clauses after purity: 0
% 8.36/1.73 % Propositional unsat core size : 0
% 8.36/1.73 % Propositional preprocessing time : 0.000
% 8.36/1.73 % Propositional encoding time : 0.000
% 8.36/1.73 % Propositional solver time : 0.000
% 8.36/1.73 % Success case prop preproc time : 0.000
% 8.36/1.73 % Success case prop encoding time : 0.000
% 8.36/1.73 % Success case prop solver time : 0.000
% 8.36/1.73 % Current number of processed clauses : 1782
% 8.36/1.73 % Positive orientable unit clauses : 351
% 8.36/1.73 % Positive unorientable unit clauses: 10
% 8.36/1.73 % Negative unit clauses : 26
% 8.36/1.73 % Non-unit-clauses : 1395
% 8.36/1.73 % Current number of unprocessed clauses: 45577
% 8.36/1.73 % ...number of literals in the above : 144543
% 8.36/1.73 % Current number of archived formulas : 0
% 8.36/1.73 % Current number of archived clauses : 103
% 8.36/1.73 % Clause-clause subsumption calls (NU) : 133603
% 8.36/1.73 % Rec. Clause-clause subsumption calls : 87543
% 8.36/1.73 % Non-unit clause-clause subsumptions : 1184
% 8.36/1.73 % Unit Clause-clause subsumption calls : 5035
% 8.36/1.73 % Rewrite failures with RHS unbound : 0
% 8.36/1.73 % BW rewrite match attempts : 768
% 8.36/1.73 % BW rewrite match successes : 120
% 8.36/1.73 % Condensation attempts : 0
% 8.36/1.73 % Condensation successes : 0
% 8.36/1.73 % Termbank termtop insertions : 1211465
% 8.36/1.73 % Search garbage collected termcells : 20548
% 8.36/1.73
% 8.36/1.73 % -------------------------------------------------
% 8.36/1.73 % User time : 1.163 s
% 8.36/1.73 % System time : 0.059 s
% 8.36/1.73 % Total time : 1.222 s
% 8.36/1.73 % Maximum resident set size: 10148 pages
% 8.36/1.73
% 8.36/1.73 % -------------------------------------------------
% 8.36/1.73 % User time : 5.486 s
% 8.36/1.73 % System time : 0.256 s
% 8.36/1.73 % Total time : 5.742 s
% 8.36/1.73 % Maximum resident set size: 6144 pages
% 8.36/1.73 % E exiting
%------------------------------------------------------------------------------