%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU406+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:25:00 PM UTC 2026
% Result : Theorem 203.77s 34.59s
% Output : CNFRefutation 203.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 48 unt; 0 def)
% Number of atoms : 199 ( 65 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 197 ( 74 ~; 74 |; 41 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 144 ( 9 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k2_xboole_0(X1,X2)) = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t46_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : k2_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t1_boole) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d4_xboole_0) ).
fof(t1_latsum_1,conjecture,
! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(t51_card_1,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+54.ax',t51_card_1) ).
fof(t3_boole,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t3_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t39_xboole_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t48_xboole_1) ).
fof(t52_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t52_xboole_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',idempotence_k3_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d2_xboole_0) ).
fof(t55_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(k2_xboole_0(X1,X2),k3_xboole_0(X1,X2)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t55_xboole_1) ).
fof(t40_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t40_xboole_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k3_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d3_xboole_0) ).
fof(c_0_15,plain,
! [X158,X159] : k4_xboole_0(X158,k2_xboole_0(X158,X159)) = k1_xboole_0,
inference(variable_rename,[status(thm)],[t46_xboole_1]) ).
fof(c_0_16,plain,
! [X381] : k2_xboole_0(X381,k1_xboole_0) = X381,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
inference(assume_negation,[status(cth)],[t1_latsum_1]) ).
cnf(c_0_19,plain,
k4_xboole_0(X1,k2_xboole_0(X1,X2)) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
np__0 = k1_xboole_0,
inference(split_conjunct,[status(thm)],[t51_card_1]) ).
cnf(c_0_21,plain,
k2_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X120] : k4_xboole_0(X120,k1_xboole_0) = X120,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_23,plain,
! [X111,X112,X113,X114,X115,X116,X117,X118] :
( ( X118 = k4_xboole_0(X116,X117)
| r2_hidden(esk11_3(X116,X117,X118),X118)
| ~ r2_hidden(esk11_3(X116,X117,X118),X117) )
& ( X118 = k4_xboole_0(X116,X117)
| r2_hidden(esk11_3(X116,X117,X118),X118)
| r2_hidden(esk11_3(X116,X117,X118),X116) )
& ( X118 = k4_xboole_0(X116,X117)
| r2_hidden(esk11_3(X116,X117,X118),X117)
| ~ r2_hidden(esk11_3(X116,X117,X118),X116)
| ~ r2_hidden(esk11_3(X116,X117,X118),X118) )
& ( X113 != k4_xboole_0(X111,X112)
| r2_hidden(X115,X113)
| r2_hidden(X115,X112)
| ~ r2_hidden(X115,X111) )
& ( X113 != k4_xboole_0(X111,X112)
| ~ r2_hidden(X114,X113)
| ~ r2_hidden(X114,X112) )
& ( X113 != k4_xboole_0(X111,X112)
| ~ r2_hidden(X114,X113)
| r2_hidden(X114,X111) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])])]) ).
fof(c_0_24,negated_conjecture,
( ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& ( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) )
& ( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) )
& r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0))
& r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_25,plain,
! [X378,X379] : k2_xboole_0(X378,X379) = k2_xboole_0(X379,X378),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_26,plain,
! [X140,X141] : k2_xboole_0(X140,k4_xboole_0(X141,X140)) = k2_xboole_0(X140,X141),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_27,plain,
! [X162,X163] : k4_xboole_0(X162,k4_xboole_0(X162,X163)) = k3_xboole_0(X162,X163),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_28,plain,
! [X172,X173,X174] : k4_xboole_0(X172,k4_xboole_0(X173,X174)) = k2_xboole_0(k4_xboole_0(X172,X173),k3_xboole_0(X172,X174)),
inference(variable_rename,[status(thm)],[t52_xboole_1]) ).
cnf(c_0_29,plain,
k4_xboole_0(X1,k2_xboole_0(X1,X2)) = np__0,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,plain,
k2_xboole_0(X1,np__0) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_31,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( X4 != k4_xboole_0(X2,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X768] : k3_xboole_0(X768,X768) = X768,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
cnf(c_0_36,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
k4_xboole_0(X1,X1) = np__0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
k4_xboole_0(X1,np__0) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_20]) ).
fof(c_0_41,plain,
! [X369,X370,X371,X372,X373,X374,X375,X376] :
( ( X376 = k2_xboole_0(X374,X375)
| r2_hidden(esk20_3(X374,X375,X376),X375)
| r2_hidden(esk20_3(X374,X375,X376),X374)
| r2_hidden(esk20_3(X374,X375,X376),X376) )
& ( X376 = k2_xboole_0(X374,X375)
| ~ r2_hidden(esk20_3(X374,X375,X376),X376)
| ~ r2_hidden(esk20_3(X374,X375,X376),X375) )
& ( X376 = k2_xboole_0(X374,X375)
| ~ r2_hidden(esk20_3(X374,X375,X376),X376)
| ~ r2_hidden(esk20_3(X374,X375,X376),X374) )
& ( X371 != k2_xboole_0(X369,X370)
| r2_hidden(X373,X371)
| ~ r2_hidden(X373,X370) )
& ( X371 != k2_xboole_0(X369,X370)
| r2_hidden(X373,X371)
| ~ r2_hidden(X373,X369) )
& ( X371 != k2_xboole_0(X369,X370)
| r2_hidden(X372,X370)
| r2_hidden(X372,X369)
| ~ r2_hidden(X372,X371) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_42,plain,
( ~ r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_43,negated_conjecture,
r2_hidden(esk2_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_44,plain,
! [X181,X182] : k4_xboole_0(k2_xboole_0(X181,X182),k3_xboole_0(X181,X182)) = k2_xboole_0(k4_xboole_0(X181,X182),k4_xboole_0(X182,X181)),
inference(variable_rename,[status(thm)],[t55_xboole_1]) ).
cnf(c_0_45,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_46,plain,
! [X142,X143] : k4_xboole_0(k2_xboole_0(X142,X143),X143) = k4_xboole_0(X142,X143),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_47,plain,
k3_xboole_0(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
k2_xboole_0(k4_xboole_0(X1,X2),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]) ).
fof(c_0_49,plain,
! [X749,X750,X751,X752,X753,X754,X755,X756] :
( ( X756 = k3_xboole_0(X754,X755)
| r2_hidden(esk50_3(X754,X755,X756),X756)
| r2_hidden(esk50_3(X754,X755,X756),X755) )
& ( X756 = k3_xboole_0(X754,X755)
| r2_hidden(esk50_3(X754,X755,X756),X756)
| r2_hidden(esk50_3(X754,X755,X756),X754) )
& ( X756 = k3_xboole_0(X754,X755)
| ~ r2_hidden(esk50_3(X754,X755,X756),X755)
| ~ r2_hidden(esk50_3(X754,X755,X756),X754)
| ~ r2_hidden(esk50_3(X754,X755,X756),X756) )
& ( X751 != k3_xboole_0(X749,X750)
| r2_hidden(X753,X751)
| ~ r2_hidden(X753,X750)
| ~ r2_hidden(X753,X749) )
& ( X751 != k3_xboole_0(X749,X750)
| ~ r2_hidden(X752,X751)
| r2_hidden(X752,X750) )
& ( X751 != k3_xboole_0(X749,X750)
| ~ r2_hidden(X752,X751)
| r2_hidden(X752,X749) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])]) ).
cnf(c_0_50,plain,
( X2 != k2_xboole_0(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( r2_hidden(esk2_0,X1)
| r2_hidden(esk2_0,k4_xboole_0(k2_xboole_0(esk4_0,esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k3_xboole_0(X1,X2)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,negated_conjecture,
r2_hidden(esk1_0,k2_xboole_0(esk4_0,esk3_0)),
inference(rw,[status(thm)],[c_0_45,c_0_34]) ).
cnf(c_0_54,plain,
k4_xboole_0(k2_xboole_0(X1,X2),X2) = k4_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_47]),c_0_48]) ).
cnf(c_0_56,plain,
( X3 != k3_xboole_0(X2,X4)
| ~ r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( r2_hidden(esk2_0,k3_xboole_0(esk4_0,esk3_0))
| r2_hidden(esk2_0,k2_xboole_0(k4_xboole_0(esk4_0,esk3_0),k4_xboole_0(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( X3 != k4_xboole_0(X2,X4)
| ~ r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_60,negated_conjecture,
( r2_hidden(esk1_0,X1)
| r2_hidden(esk1_0,k4_xboole_0(k2_xboole_0(esk4_0,esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_53]) ).
cnf(c_0_61,plain,
k4_xboole_0(k2_xboole_0(X1,X2),k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_36]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ r2_hidden(X1,k3_xboole_0(X2,X3))
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( r2_hidden(esk2_0,k4_xboole_0(esk4_0,esk3_0))
| r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| r2_hidden(esk2_0,k3_xboole_0(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_66,negated_conjecture,
( r2_hidden(esk1_0,esk4_0)
| r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0))
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_68,negated_conjecture,
( r2_hidden(esk2_0,esk4_0)
| r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_69,negated_conjecture,
~ r2_hidden(esk2_0,k4_xboole_0(esk3_0,esk4_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_71,negated_conjecture,
r2_hidden(esk2_0,esk4_0),
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( ~ r2_hidden(esk2_0,esk4_0)
| ~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_73,negated_conjecture,
~ r2_hidden(esk1_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
cnf(c_0_74,negated_conjecture,
~ r2_hidden(esk1_0,k4_xboole_0(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_71])]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_66,c_0_73]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.55 % Computer : n005.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Mon Sep 21 06:21:05 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.14/0.55 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.60 Running first-order theorem proving
% 0.14/0.60 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
% 203.77/34.59 % Version: 3.5.1
% 203.77/34.59 % Preprocessing class: FMLLMLLLSSSNFFN.
% 203.77/34.59 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 203.77/34.59 % Starting new_bool_3 with 888s (3) cores
% 203.77/34.59 % Starting new_bool_1 with 888s (3) cores
% 203.77/34.59 % Starting sh5l with 296s (1) cores
% 203.77/34.59 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 296s (1) cores
% 203.77/34.59 % new_bool_1 with pid 2748482 completed with status 0
% 203.77/34.59 % Result found by new_bool_1
% 203.77/34.59 % Preprocessing class: FMLLMLLLSSSNFFN.
% 203.77/34.59 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 203.77/34.59 % Starting new_bool_3 with 888s (3) cores
% 203.77/34.59 % Starting new_bool_1 with 888s (3) cores
% 203.77/34.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 203.77/34.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 203.77/34.59 % Search class: FGHSM-SMLM32-DFFFFFNN
% 203.77/34.59 % Scheduled 13 strats onto 3 cores with 887 seconds (887 total)
% 203.77/34.59 % Starting SubtermCWHack with 80s (1) cores
% 203.77/34.59 % Starting new_bool_1 with 89s (1) cores
% 203.77/34.59 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 67s (1) cores
% 203.77/34.59 % new_bool_1 with pid 2748494 completed with status 0
% 203.77/34.59 % Result found by new_bool_1
% 203.77/34.59 % Preprocessing class: FMLLMLLLSSSNFFN.
% 203.77/34.59 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 203.77/34.59 % Starting new_bool_3 with 888s (3) cores
% 203.77/34.59 % Starting new_bool_1 with 888s (3) cores
% 203.77/34.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 203.77/34.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 203.77/34.59 % Search class: FGHSM-SMLM32-DFFFFFNN
% 203.77/34.59 % Scheduled 13 strats onto 3 cores with 887 seconds (887 total)
% 203.77/34.59 % Starting SubtermCWHack with 80s (1) cores
% 203.77/34.59 % Starting new_bool_1 with 89s (1) cores
% 203.77/34.59 % Preprocessing time : 0.310 s
% 203.77/34.59 % Presaturation interreduction done
% 203.77/34.59
% 203.77/34.59 % Proof found!
% 203.77/34.59 % SZS status Theorem
% 203.77/34.59 % SZS output start CNFRefutation
% See solution above
% 203.77/34.59 % Parsed axioms : 66033
% 203.77/34.59 % Removed by relevancy pruning/SinE : 63943
% 203.77/34.59 % Initial clauses : 4175
% 203.77/34.59 % Removed in clause preprocessing : 66
% 203.77/34.59 % Initial clauses in saturation : 4109
% 203.77/34.59 % Processed clauses : 40065
% 203.77/34.59 % ...of these trivial : 601
% 203.77/34.59 % ...subsumed : 24544
% 203.77/34.59 % ...remaining for further processing : 14919
% 203.77/34.59 % Other redundant clauses eliminated : 3088
% 203.77/34.59 % Clauses deleted for lack of memory : 0
% 203.77/34.59 % Backward-subsumed : 80
% 203.77/34.59 % Backward-rewritten : 633
% 203.77/34.59 % Generated clauses : 226007
% 203.77/34.59 % ...of the previous two non-redundant : 205122
% 203.77/34.59 % ...aggressively subsumed : 0
% 203.77/34.59 % Contextual simplify-reflections : 295
% 203.77/34.59 % Paramodulations : 222760
% 203.77/34.59 % Factorizations : 34
% 203.77/34.59 % NegExts : 0
% 203.77/34.59 % Equation resolutions : 3209
% 203.77/34.59 % Disequality decompositions : 0
% 203.77/34.59 % Total rewrite steps : 56870
% 203.77/34.59 % ...of those cached : 50780
% 203.77/34.59 % Propositional unsat checks : 2
% 203.77/34.59 % Propositional check models : 1
% 203.77/34.59 % Propositional check unsatisfiable : 0
% 203.77/34.59 % Propositional clauses : 0
% 203.77/34.59 % Propositional clauses after purity: 0
% 203.77/34.59 % Propositional unsat core size : 0
% 203.77/34.59 % Propositional preprocessing time : 0.000
% 203.77/34.59 % Propositional encoding time : 0.277
% 203.77/34.59 % Propositional solver time : 0.286
% 203.77/34.59 % Success case prop preproc time : 0.000
% 203.77/34.59 % Success case prop encoding time : 0.000
% 203.77/34.59 % Success case prop solver time : 0.000
% 203.77/34.59 % Current number of processed clauses : 10255
% 203.77/34.59 % Positive orientable unit clauses : 2187
% 203.77/34.59 % Positive unorientable unit clauses: 3
% 203.77/34.59 % Negative unit clauses : 3049
% 203.77/34.59 % Non-unit-clauses : 5016
% 203.77/34.59 % Current number of unprocessed clauses: 172014
% 203.77/34.59 % ...number of literals in the above : 721913
% 203.77/34.59 % Current number of archived formulas : 0
% 203.77/34.59 % Current number of archived clauses : 4429
% 203.77/34.59 % Clause-clause subsumption calls (NU) : 15473746
% 203.77/34.59 % Rec. Clause-clause subsumption calls : 2597071
% 203.77/34.59 % Non-unit clause-clause subsumptions : 5922
% 203.77/34.59 % Unit Clause-clause subsumption calls : 1588297
% 203.77/34.59 % Rewrite failures with RHS unbound : 0
% 203.77/34.59 % BW rewrite match attempts : 593
% 203.77/34.59 % BW rewrite match successes : 379
% 203.77/34.59 % Condensation attempts : 0
% 203.77/34.59 % Condensation successes : 0
% 203.77/34.59 % Termbank termtop insertions : 6205545
% 203.77/34.59 % Search garbage collected termcells : 774327
% 203.77/34.59
% 203.77/34.59 % -------------------------------------------------
% 203.77/34.59 % User time : 27.261 s
% 203.77/34.59 % System time : 0.768 s
% 203.77/34.59 % Total time : 28.030 s
% 203.77/34.59 % Maximum resident set size: 139104 pages
% 203.77/34.59
% 203.77/34.59 % -------------------------------------------------
% 203.77/34.59 % User time : 85.493 s
% 203.77/34.59 % System time : 2.151 s
% 203.77/34.59 % Total time : 87.644 s
% 203.77/34.59 % Maximum resident set size: 112384 pages
% 203.77/34.59 % E exiting
%------------------------------------------------------------------------------