%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO507+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:28:22 PM UTC 2026
% Result : Theorem 106.09s 15.99s
% Output : CNFRefutation 106.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 95 ( 27 unt; 0 def)
% Number of atoms : 387 ( 93 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 480 ( 188 ~; 233 |; 59 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 241 ( 11 sgn 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz8_14a,conjecture,
! [X12,X15,X13,X16] :
( ~ s_col(X12,X15,X16)
| ~ s_col(X12,X15,X13)
| ~ perp(X12,X15,X13,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14a) ).
fof(d_Defn8_11b,axiom,
! [X13,X16,X42,X43,X1] :
( ( ~ perpAt(X13,X16,X1,X42,X43)
| perp(X13,X16,X42,X43) )
& ( perpAt(X13,X16,il(X13,X16,X42,X43),X42,X43)
| ~ perp(X13,X16,X42,X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11b) ).
fof(d_Defn8_11a,axiom,
! [X2,X3,X1,X9,X10,X35,X4] :
( ( ~ s_r(f811(X2,X3,X9,X10,X1),X1,g811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X9,X10,g811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X2,X3,f811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_r(X35,X1,X4)
| ~ s_col(X9,X10,X4)
| ~ s_col(X2,X3,X35)
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( X9 != X10
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( X2 != X3
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X9,X10,X1)
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X2,X3,X1)
| ~ perpAt(X2,X3,X1,X9,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11a) ).
fof(aSatz4_12b,axiom,
! [X12,X15] : s_col(X12,X15,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
fof(aSatz8_2,axiom,
! [X12,X15,X14] :
( s_r(X14,X15,X12)
| ~ s_r(X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_2) ).
fof(aSatz8_7,axiom,
! [X12,X15,X14] :
( X15 = X14
| ~ s_r(X12,X14,X15)
| ~ s_r(X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_7) ).
fof(aSatz8_5,axiom,
! [X12,X15] : s_r(X12,X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_5) ).
fof(d_Defn4_10,axiom,
! [X12,X15,X14] :
( ( ~ s_t(X14,X12,X15)
| s_col(X12,X15,X14) )
& ( ~ s_t(X15,X14,X12)
| s_col(X12,X15,X14) )
& ( ~ s_t(X12,X15,X14)
| s_col(X12,X15,X14) )
& ( s_t(X14,X12,X15)
| s_t(X15,X14,X12)
| s_t(X12,X15,X14)
| ~ s_col(X12,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_10) ).
fof(aSatz6_18,axiom,
! [X12,X15,X13,X16,X27] :
( s_col(X12,X15,X27)
| ~ s_col(X13,X16,X27)
| ~ s_col(X13,X16,X15)
| ~ s_col(X13,X16,X12)
| X13 = X16
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_18) ).
fof(aSatz4_11d,axiom,
! [X12,X15,X14] :
( s_col(X15,X12,X14)
| ~ s_col(X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11d) ).
fof(aSatz3_3,axiom,
! [X20,X21] : s_t(X20,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
fof(aSatz6_16b,axiom,
! [X13,X16,X28,X27] :
( s_col(X13,X28,X27)
| ~ s_col(X13,X16,X27)
| ~ s_col(X13,X16,X28)
| X28 = X13
| X13 = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16b) ).
fof(aSatz8_12b,axiom,
! [X12,X15,X13,X16] :
( perp(X13,X16,X12,X15)
| ~ perp(X12,X15,X13,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12b) ).
fof(aSatz8_9,axiom,
! [X12,X15,X14] :
( X14 = X15
| X12 = X15
| ~ s_col(X12,X15,X14)
| ~ s_r(X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_9) ).
fof(aSatz4_11c,axiom,
! [X12,X15,X14] :
( s_col(X14,X15,X12)
| ~ s_col(X12,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11c) ).
fof(aSatz8_13a,axiom,
! [X12,X15,X14,X13,X16] :
( ( s_r(f813(X12,X15,X13,X16,X14),X14,g813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X14 != g813(X12,X15,X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X14 != f813(X12,X15,X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X13,X16,g813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X12,X15,f813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X12,X15,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X13 != X16
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X12 != X15
| ~ perpAt(X12,X15,X14,X13,X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13a) ).
fof(c_0_16,negated_conjecture,
~ ! [X12,X15,X13,X16] :
( ~ s_col(X12,X15,X16)
| ~ s_col(X12,X15,X13)
| ~ perp(X12,X15,X13,X16) ),
inference(assume_negation,[status(cth)],[aSatz8_14a]) ).
fof(c_0_17,plain,
! [X13,X16,X42,X43,X1] :
( ( ~ perpAt(X13,X16,X1,X42,X43)
| perp(X13,X16,X42,X43) )
& ( perpAt(X13,X16,il(X13,X16,X42,X43),X42,X43)
| ~ perp(X13,X16,X42,X43) ) ),
inference(fof_simplification,[status(thm)],[d_Defn8_11b]) ).
fof(c_0_18,negated_conjecture,
~ ! [X12,X15,X13,X16] :
( ~ s_col(X12,X15,X16)
| ~ s_col(X12,X15,X13)
| ~ perp(X12,X15,X13,X16) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X2,X3,X1,X9,X10,X35,X4] :
( ( ~ s_r(f811(X2,X3,X9,X10,X1),X1,g811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X9,X10,g811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X2,X3,f811(X2,X3,X9,X10,X1))
| ~ s_col(X9,X10,X1)
| ~ s_col(X2,X3,X1)
| X9 = X10
| X2 = X3
| perpAt(X2,X3,X1,X9,X10) )
& ( s_r(X35,X1,X4)
| ~ s_col(X9,X10,X4)
| ~ s_col(X2,X3,X35)
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( X9 != X10
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( X2 != X3
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X9,X10,X1)
| ~ perpAt(X2,X3,X1,X9,X10) )
& ( s_col(X2,X3,X1)
| ~ perpAt(X2,X3,X1,X9,X10) ) ),
inference(fof_simplification,[status(thm)],[d_Defn8_11a]) ).
fof(c_0_20,plain,
! [X607,X608,X609,X610,X611] :
( ( ~ perpAt(X607,X608,X611,X609,X610)
| perp(X607,X608,X609,X610) )
& ( perpAt(X607,X608,il(X607,X608,X609,X610),X609,X610)
| ~ perp(X607,X608,X609,X610) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_21,negated_conjecture,
( s_col(esk1_0,esk2_0,esk4_0)
& s_col(esk1_0,esk2_0,esk3_0)
& perp(esk1_0,esk2_0,esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_22,plain,
! [X600,X601,X602,X603,X604,X605,X606] :
( ( ~ s_r(f811(X600,X601,X603,X604,X602),X602,g811(X600,X601,X603,X604,X602))
| ~ s_col(X603,X604,X602)
| ~ s_col(X600,X601,X602)
| X603 = X604
| X600 = X601
| perpAt(X600,X601,X602,X603,X604) )
& ( s_col(X603,X604,g811(X600,X601,X603,X604,X602))
| ~ s_col(X603,X604,X602)
| ~ s_col(X600,X601,X602)
| X603 = X604
| X600 = X601
| perpAt(X600,X601,X602,X603,X604) )
& ( s_col(X600,X601,f811(X600,X601,X603,X604,X602))
| ~ s_col(X603,X604,X602)
| ~ s_col(X600,X601,X602)
| X603 = X604
| X600 = X601
| perpAt(X600,X601,X602,X603,X604) )
& ( s_r(X605,X602,X606)
| ~ s_col(X603,X604,X606)
| ~ s_col(X600,X601,X605)
| ~ perpAt(X600,X601,X602,X603,X604) )
& ( X603 != X604
| ~ perpAt(X600,X601,X602,X603,X604) )
& ( X600 != X601
| ~ perpAt(X600,X601,X602,X603,X604) )
& ( s_col(X603,X604,X602)
| ~ perpAt(X600,X601,X602,X603,X604) )
& ( s_col(X600,X601,X602)
| ~ perpAt(X600,X601,X602,X603,X604) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
cnf(c_0_23,plain,
( ~ perp(X1,X2,X3,X4)
| perpAt(X1,X2,il(X1,X2,X3,X4),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
perp(esk1_0,esk2_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( ~ s_col(X4,X5,X7)
| ~ s_col(X1,X2,X6)
| ~ perpAt(X1,X2,X3,X4,X5)
| s_r(X6,X3,X7) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
perpAt(esk1_0,esk2_0,il(esk1_0,esk2_0,esk3_0,esk4_0),esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_27,plain,
! [X206,X207] : s_col(X206,X207,X206),
inference(variable_rename,[status(thm)],[aSatz4_12b]) ).
fof(c_0_28,plain,
! [X12,X15,X14] :
( s_r(X14,X15,X12)
| ~ s_r(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz8_2]) ).
fof(c_0_29,plain,
! [X12,X15,X14] :
( X15 = X14
| ~ s_r(X12,X14,X15)
| ~ s_r(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz8_7]) ).
cnf(c_0_30,negated_conjecture,
( ~ s_col(esk1_0,esk2_0,X1)
| ~ s_col(esk3_0,esk4_0,X2)
| s_r(X1,il(esk1_0,esk2_0,esk3_0,esk4_0),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
s_col(X1,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_32,plain,
! [X487,X488,X489] :
( s_r(X489,X488,X487)
| ~ s_r(X487,X488,X489) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_33,plain,
! [X497,X498] : s_r(X497,X498,X498),
inference(variable_rename,[status(thm)],[aSatz8_5]) ).
fof(c_0_34,plain,
! [X503,X504,X505] :
( X504 = X505
| ~ s_r(X503,X505,X504)
| ~ s_r(X503,X504,X505) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
( ~ s_col(esk1_0,esk2_0,X1)
| s_r(X1,il(esk1_0,esk2_0,esk3_0,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
s_col(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,plain,
( ~ s_r(X1,X2,X3)
| s_r(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
s_r(X1,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X12,X15,X14] :
( ( ~ s_t(X14,X12,X15)
| s_col(X12,X15,X14) )
& ( ~ s_t(X15,X14,X12)
| s_col(X12,X15,X14) )
& ( ~ s_t(X12,X15,X14)
| s_col(X12,X15,X14) )
& ( s_t(X14,X12,X15)
| s_t(X15,X14,X12)
| s_t(X12,X15,X14)
| ~ s_col(X12,X15,X14) ) ),
inference(fof_simplification,[status(thm)],[d_Defn4_10]) ).
fof(c_0_40,plain,
! [X12,X15,X13,X16,X27] :
( s_col(X12,X15,X27)
| ~ s_col(X13,X16,X27)
| ~ s_col(X13,X16,X15)
| ~ s_col(X13,X16,X12)
| X13 = X16
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz6_18]) ).
fof(c_0_41,plain,
! [X12,X15,X14] :
( s_col(X15,X12,X14)
| ~ s_col(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz4_11d]) ).
cnf(c_0_42,plain,
( ~ s_r(X1,X3,X2)
| ~ s_r(X1,X2,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
s_r(esk3_0,il(esk1_0,esk2_0,esk3_0,esk4_0),esk3_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
s_r(X1,X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_45,plain,
! [X568,X569,X570] :
( ( ~ s_t(X570,X568,X569)
| s_col(X568,X569,X570) )
& ( ~ s_t(X569,X570,X568)
| s_col(X568,X569,X570) )
& ( ~ s_t(X568,X569,X570)
| s_col(X568,X569,X570) )
& ( s_t(X570,X568,X569)
| s_t(X569,X570,X568)
| s_t(X568,X569,X570)
| ~ s_col(X568,X569,X570) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
fof(c_0_46,plain,
! [X125,X126] : s_t(X125,X125,X126),
inference(variable_rename,[status(thm)],[aSatz3_3]) ).
fof(c_0_47,plain,
! [X375,X376,X377,X378,X379] :
( s_col(X375,X376,X379)
| ~ s_col(X377,X378,X379)
| ~ s_col(X377,X378,X376)
| ~ s_col(X377,X378,X375)
| X377 = X378
| X375 = X376 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
fof(c_0_48,plain,
! [X198,X199,X200] :
( s_col(X199,X198,X200)
| ~ s_col(X198,X199,X200) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_41])]) ).
cnf(c_0_49,negated_conjecture,
il(esk1_0,esk2_0,esk3_0,esk4_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_50,plain,
( ~ s_t(X2,X3,X1)
| s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
s_t(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_52,plain,
! [X13,X16,X28,X27] :
( s_col(X13,X28,X27)
| ~ s_col(X13,X16,X27)
| ~ s_col(X13,X16,X28)
| X28 = X13
| X13 = X16 ),
inference(fof_simplification,[status(thm)],[aSatz6_16b]) ).
cnf(c_0_53,plain,
( ~ s_col(X3,X4,X5)
| ~ s_col(X3,X4,X2)
| ~ s_col(X3,X4,X1)
| s_col(X1,X2,X5)
| X3 = X4
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( ~ s_col(X1,X2,X3)
| s_col(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_55,plain,
! [X12,X15,X13,X16] :
( perp(X13,X16,X12,X15)
| ~ perp(X12,X15,X13,X16) ),
inference(fof_simplification,[status(thm)],[aSatz8_12b]) ).
fof(c_0_56,plain,
! [X12,X15,X14] :
( X14 = X15
| X12 = X15
| ~ s_col(X12,X15,X14)
| ~ s_r(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz8_9]) ).
cnf(c_0_57,negated_conjecture,
( ~ s_col(esk1_0,esk2_0,X1)
| ~ s_col(esk3_0,esk4_0,X2)
| s_r(X1,esk3_0,X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_58,plain,
s_col(X1,X2,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_59,plain,
! [X366,X367,X368,X369] :
( s_col(X366,X368,X369)
| ~ s_col(X366,X367,X369)
| ~ s_col(X366,X367,X368)
| X368 = X366
| X366 = X367 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_52])]) ).
fof(c_0_60,plain,
! [X12,X15,X14] :
( s_col(X14,X15,X12)
| ~ s_col(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz4_11c]) ).
cnf(c_0_61,plain,
( ~ s_col(X3,X4,X1)
| ~ s_col(X3,X4,X2)
| s_col(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_53,c_0_31]) ).
cnf(c_0_62,negated_conjecture,
s_col(esk2_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_54,c_0_36]) ).
cnf(c_0_63,negated_conjecture,
s_col(esk1_0,esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_64,plain,
! [X522,X523,X524,X525] :
( perp(X524,X525,X522,X523)
| ~ perp(X522,X523,X524,X525) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_55])]) ).
fof(c_0_65,plain,
! [X508,X509,X510] :
( X510 = X509
| X508 = X509
| ~ s_col(X508,X509,X510)
| ~ s_r(X508,X509,X510) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_56])]) ).
cnf(c_0_66,negated_conjecture,
( ~ s_col(esk1_0,esk2_0,X1)
| s_r(X1,esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
( ~ s_col(X1,X2,X4)
| ~ s_col(X1,X2,X3)
| s_col(X1,X3,X4)
| X3 = X1
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_68,plain,
! [X12,X15,X14,X13,X16] :
( ( s_r(f813(X12,X15,X13,X16,X14),X14,g813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X14 != g813(X12,X15,X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X14 != f813(X12,X15,X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X13,X16,g813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X12,X15,f813(X12,X15,X13,X16,X14))
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X12,X15,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( s_col(X13,X16,X14)
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X13 != X16
| ~ perpAt(X12,X15,X14,X13,X16) )
& ( X12 != X15
| ~ perpAt(X12,X15,X14,X13,X16) ) ),
inference(fof_simplification,[status(thm)],[aSatz8_13a]) ).
fof(c_0_69,plain,
! [X195,X196,X197] :
( s_col(X197,X196,X195)
| ~ s_col(X195,X196,X197) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_60])]) ).
cnf(c_0_70,negated_conjecture,
( ~ s_col(esk2_0,esk1_0,X1)
| s_col(X1,esk3_0,esk2_0)
| X1 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
s_col(esk2_0,esk1_0,esk4_0),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_72,plain,
( ~ perp(X1,X2,X3,X4)
| perp(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
( ~ s_col(X1,X2,X3)
| ~ s_r(X1,X2,X3)
| X3 = X2
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,negated_conjecture,
s_r(esk1_0,esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_75,negated_conjecture,
( ~ s_col(esk1_0,esk2_0,X1)
| s_col(esk1_0,X1,esk4_0)
| esk1_0 = X1
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_63]) ).
fof(c_0_76,plain,
! [X526,X527,X528,X529,X530] :
( ( s_r(f813(X526,X527,X529,X530,X528),X528,g813(X526,X527,X529,X530,X528))
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( X528 != g813(X526,X527,X529,X530,X528)
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( X528 != f813(X526,X527,X529,X530,X528)
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( s_col(X529,X530,g813(X526,X527,X529,X530,X528))
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( s_col(X526,X527,f813(X526,X527,X529,X530,X528))
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( s_col(X526,X527,X528)
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( s_col(X529,X530,X528)
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( X529 != X530
| ~ perpAt(X526,X527,X528,X529,X530) )
& ( X526 != X527
| ~ perpAt(X526,X527,X528,X529,X530) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).
cnf(c_0_77,negated_conjecture,
s_r(esk2_0,esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_66,c_0_58]) ).
cnf(c_0_78,plain,
( ~ s_col(X1,X2,X3)
| s_col(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( s_col(esk4_0,esk3_0,esk2_0)
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
perp(esk3_0,esk4_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_72,c_0_24]) ).
cnf(c_0_81,negated_conjecture,
( ~ s_col(esk1_0,esk3_0,esk4_0)
| esk4_0 = esk3_0
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( s_col(esk1_0,esk3_0,esk4_0)
| esk2_0 = esk1_0
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_36]) ).
cnf(c_0_83,plain,
( X1 != X2
| ~ perpAt(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( ~ s_col(esk2_0,esk3_0,esk4_0)
| esk4_0 = esk3_0
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( s_col(esk2_0,esk3_0,esk4_0)
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
perpAt(esk3_0,esk4_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_23,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( esk3_0 = esk1_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,plain,
~ perpAt(X1,X1,X2,X3,X4),
inference(er,[status(thm)],[c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( esk3_0 = esk2_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( esk2_0 = esk1_0
| esk3_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( esk2_0 = esk1_0
| esk3_0 = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_89]),c_0_88]) ).
cnf(c_0_92,negated_conjecture,
perpAt(esk1_0,esk2_0,esk3_0,esk3_0,esk4_0),
inference(rw,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_93,negated_conjecture,
esk2_0 = esk1_0,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO507+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 20 16:57:04 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 106.09/15.99 % Version: 3.5.1
% 106.09/15.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 106.09/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.09/15.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 106.09/15.99 % Starting new_bool_3 with 300s (1) cores
% 106.09/15.99 % Starting new_bool_1 with 300s (1) cores
% 106.09/15.99 % Starting sh5l with 300s (1) cores
% 106.09/15.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3209039 completed with status 0
% 106.09/15.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 106.09/15.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 106.09/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.09/15.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 106.09/15.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.09/15.99 % No SInE strategy applied
% 106.09/15.99 % Search class: FGHSM-FSLS33-MFFFFFNN
% 106.09/15.99 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 106.09/15.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 106.09/15.99 % Starting SubtermCWHack with 136s (1) cores
% 106.09/15.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 106.09/15.99 % Starting new_bool_3 with 393s (1) cores
% 106.09/15.99 % Starting G-E--_303_C18_F1_URBAN_S0Y with 330s (1) cores
% 106.09/15.99 % Starting Y1006__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 106.09/15.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3209047 completed with status 0
% 106.09/15.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 106.09/15.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 106.09/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.09/15.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 106.09/15.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.09/15.99 % No SInE strategy applied
% 106.09/15.99 % Search class: FGHSM-FSLS33-MFFFFFNN
% 106.09/15.99 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 106.09/15.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 106.09/15.99 % Starting SubtermCWHack with 136s (1) cores
% 106.09/15.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 106.09/15.99 % Preprocessing time : 0.004 s
% 106.09/15.99 % Presaturation interreduction done
% 106.09/15.99
% 106.09/15.99 % Proof found!
% 106.09/15.99 % SZS status Theorem
% 106.09/15.99 % SZS output start CNFRefutation
% See solution above
% 106.09/15.99 % Parsed axioms : 144
% 106.09/15.99 % Removed by relevancy pruning/SinE : 0
% 106.09/15.99 % Initial clauses : 213
% 106.09/15.99 % Removed in clause preprocessing : 1
% 106.09/15.99 % Initial clauses in saturation : 212
% 106.09/15.99 % Processed clauses : 23581
% 106.09/15.99 % ...of these trivial : 292
% 106.09/15.99 % ...subsumed : 15744
% 106.09/15.99 % ...remaining for further processing : 7545
% 106.09/15.99 % Other redundant clauses eliminated : 15
% 106.09/15.99 % Clauses deleted for lack of memory : 0
% 106.09/15.99 % Backward-subsumed : 2127
% 106.09/15.99 % Backward-rewritten : 3493
% 106.09/15.99 % Generated clauses : 484665
% 106.09/15.99 % ...of the previous two non-redundant : 470103
% 106.09/15.99 % ...aggressively subsumed : 0
% 106.09/15.99 % Contextual simplify-reflections : 213
% 106.09/15.99 % Paramodulations : 484643
% 106.09/15.99 % Factorizations : 4
% 106.09/15.99 % NegExts : 0
% 106.09/15.99 % Equation resolutions : 18
% 106.09/15.99 % Disequality decompositions : 0
% 106.09/15.99 % Total rewrite steps : 30174
% 106.09/15.99 % ...of those cached : 27754
% 106.09/15.99 % Propositional unsat checks : 1
% 106.09/15.99 % Propositional check models : 0
% 106.09/15.99 % Propositional check unsatisfiable : 0
% 106.09/15.99 % Propositional clauses : 0
% 106.09/15.99 % Propositional clauses after purity: 0
% 106.09/15.99 % Propositional unsat core size : 0
% 106.09/15.99 % Propositional preprocessing time : 0.000
% 106.09/15.99 % Propositional encoding time : 0.341
% 106.09/15.99 % Propositional solver time : 0.397
% 106.09/15.99 % Success case prop preproc time : 0.000
% 106.09/15.99 % Success case prop encoding time : 0.000
% 106.09/15.99 % Success case prop solver time : 0.000
% 106.09/15.99 % Current number of processed clauses : 1718
% 106.09/15.99 % Positive orientable unit clauses : 334
% 106.09/15.99 % Positive unorientable unit clauses: 0
% 106.09/15.99 % Negative unit clauses : 11
% 106.09/15.99 % Non-unit-clauses : 1373
% 106.09/15.99 % Current number of unprocessed clauses: 446558
% 106.09/15.99 % ...number of literals in the above : 2329649
% 106.09/15.99 % Current number of archived formulas : 0
% 106.09/15.99 % Current number of archived clauses : 5816
% 106.09/15.99 % Clause-clause subsumption calls (NU) : 5962723
% 106.09/15.99 % Rec. Clause-clause subsumption calls : 794582
% 106.09/15.99 % Non-unit clause-clause subsumptions : 18078
% 106.09/15.99 % Unit Clause-clause subsumption calls : 125147
% 106.09/15.99 % Rewrite failures with RHS unbound : 0
% 106.09/15.99 % BW rewrite match attempts : 30391
% 106.09/15.99 % BW rewrite match successes : 23
% 106.09/15.99 % Condensation attempts : 0
% 106.09/15.99 % Condensation successes : 0
% 106.09/15.99 % Termbank termtop insertions : 13577576
% 106.09/15.99 % Search garbage collected termcells : 1565
% 106.09/15.99
% 106.09/15.99 % -------------------------------------------------
% 106.09/15.99 % User time : 14.585 s
% 106.09/15.99 % System time : 0.427 s
% 106.09/15.99 % Total time : 15.012 s
% 106.09/15.99 % Maximum resident set size: 4404 pages
% 106.09/15.99
% 106.09/15.99 % -------------------------------------------------
% 106.09/15.99 % User time : 73.402 s
% 106.09/15.99 % System time : 1.988 s
% 106.09/15.99 % Total time : 75.390 s
% 106.09/15.99 % Maximum resident set size: 4864 pages
% 106.09/15.99 % E exiting
%------------------------------------------------------------------------------