%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO507+1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:21:26 PM UTC 2026
% Result : Theorem 219.01s 146.46s
% Output : CNFRefutation 219.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 16 unt; 0 def)
% Number of atoms : 397 ( 141 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 477 ( 173 ~; 254 |; 50 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 230 ( 19 sgn 133 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz6_16b,axiom,
! [X13,X16,X28,X27] :
( X13 = X16
| X28 = X13
| ~ s_col(X13,X16,X28)
| ~ s_col(X13,X16,X27)
| s_col(X13,X28,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_16b) ).
fof(aSatz8_14a,conjecture,
! [X12,X15,X13,X16] :
( ~ perp(X12,X15,X13,X16)
| ~ s_col(X12,X15,X13)
| ~ s_col(X12,X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_14a) ).
fof(aSatz8_13a,axiom,
! [X12,X15,X14,X13,X16] :
( ( ~ perpAt(X12,X15,X14,X13,X16)
| X12 != X15 )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| X13 != X16 )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_col(X13,X16,X14) )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_col(X12,X15,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(X13,X16,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)
| X14 != g813(X12,X15,X13,X16,X14) )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_r(f813(X12,X15,X13,X16,X14),X14,g813(X12,X15,X13,X16,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_13a) ).
fof(d_Defn8_11b,axiom,
! [X13,X16,X42,X43,X1] :
( ( ~ perp(X13,X16,X42,X43)
| perpAt(X13,X16,il(X13,X16,X42,X43),X42,X43) )
& ( perp(X13,X16,X42,X43)
| ~ perpAt(X13,X16,X1,X42,X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11b) ).
fof(aSatz6_18,axiom,
! [X12,X15,X13,X16,X27] :
( X12 = X15
| X13 = X16
| ~ s_col(X13,X16,X12)
| ~ s_col(X13,X16,X15)
| ~ s_col(X13,X16,X27)
| s_col(X12,X15,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz6_18) ).
fof(aSatz4_11c,axiom,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X15,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11c) ).
fof(aSatz8_12b,axiom,
! [X12,X15,X13,X16] :
( ~ perp(X12,X15,X13,X16)
| perp(X13,X16,X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_12b) ).
fof(aSatz4_12,axiom,
! [X12,X15] : s_col(X12,X12,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12) ).
fof(d_Defn8_11a,axiom,
! [X2,X3,X1,X9,X10,X35,X4] :
( ( ~ perpAt(X2,X3,X1,X9,X10)
| s_col(X2,X3,X1) )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| s_col(X9,X10,X1) )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| X2 != X3 )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| X9 != X10 )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| ~ s_col(X2,X3,X35)
| ~ s_col(X9,X10,X4)
| s_r(X35,X1,X4) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| s_col(X2,X3,f811(X2,X3,X9,X10,X1)) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| s_col(X9,X10,g811(X2,X3,X9,X10,X1)) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| ~ s_r(f811(X2,X3,X9,X10,X1),X1,g811(X2,X3,X9,X10,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn8_11a) ).
fof(aSatz8_9,axiom,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| ~ s_col(X12,X15,X14)
| X12 = X15
| X14 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_9) ).
fof(aSatz4_11b,axiom,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_11b) ).
fof(aSatz4_12b,axiom,
! [X12,X15] : s_col(X12,X15,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
fof(c_0_12,plain,
! [X13,X16,X28,X27] :
( X13 = X16
| X28 = X13
| ~ s_col(X13,X16,X28)
| ~ s_col(X13,X16,X27)
| s_col(X13,X28,X27) ),
inference(fof_simplification,[status(thm)],[aSatz6_16b]) ).
fof(c_0_13,negated_conjecture,
~ ! [X12,X15,X13,X16] :
( ~ perp(X12,X15,X13,X16)
| ~ s_col(X12,X15,X13)
| ~ s_col(X12,X15,X16) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[aSatz8_14a])]) ).
fof(c_0_14,plain,
! [X12,X15,X14,X13,X16] :
( ( ~ perpAt(X12,X15,X14,X13,X16)
| X12 != X15 )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| X13 != X16 )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_col(X13,X16,X14) )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_col(X12,X15,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(X13,X16,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)
| X14 != g813(X12,X15,X13,X16,X14) )
& ( ~ perpAt(X12,X15,X14,X13,X16)
| s_r(f813(X12,X15,X13,X16,X14),X14,g813(X12,X15,X13,X16,X14)) ) ),
inference(fof_simplification,[status(thm)],[aSatz8_13a]) ).
fof(c_0_15,plain,
! [X13,X16,X42,X43,X1] :
( ( ~ perp(X13,X16,X42,X43)
| perpAt(X13,X16,il(X13,X16,X42,X43),X42,X43) )
& ( perp(X13,X16,X42,X43)
| ~ perpAt(X13,X16,X1,X42,X43) ) ),
inference(fof_simplification,[status(thm)],[d_Defn8_11b]) ).
fof(c_0_16,plain,
! [X12,X15,X13,X16,X27] :
( X12 = X15
| X13 = X16
| ~ s_col(X13,X16,X12)
| ~ s_col(X13,X16,X15)
| ~ s_col(X13,X16,X27)
| s_col(X12,X15,X27) ),
inference(fof_simplification,[status(thm)],[aSatz6_18]) ).
fof(c_0_17,plain,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X15,X12) ),
inference(fof_simplification,[status(thm)],[aSatz4_11c]) ).
fof(c_0_18,plain,
! [X934,X935,X936,X937] :
( X934 = X935
| X936 = X934
| ~ s_col(X934,X935,X936)
| ~ s_col(X934,X935,X937)
| s_col(X934,X936,X937) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
fof(c_0_19,negated_conjecture,
( perp(esk1_0,esk2_0,esk3_0,esk4_0)
& s_col(esk1_0,esk2_0,esk3_0)
& s_col(esk1_0,esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_20,plain,
! [X1094,X1095,X1096,X1097,X1098] :
( ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| X1094 != X1095 )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| X1097 != X1098 )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| s_col(X1097,X1098,X1096) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| s_col(X1094,X1095,X1096) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| s_col(X1094,X1095,f813(X1094,X1095,X1097,X1098,X1096)) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| s_col(X1097,X1098,g813(X1094,X1095,X1097,X1098,X1096)) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| X1096 != f813(X1094,X1095,X1097,X1098,X1096) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| X1096 != g813(X1094,X1095,X1097,X1098,X1096) )
& ( ~ perpAt(X1094,X1095,X1096,X1097,X1098)
| s_r(f813(X1094,X1095,X1097,X1098,X1096),X1096,g813(X1094,X1095,X1097,X1098,X1096)) ) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X1175,X1176,X1177,X1178,X1179] :
( ( ~ perp(X1175,X1176,X1177,X1178)
| perpAt(X1175,X1176,il(X1175,X1176,X1177,X1178),X1177,X1178) )
& ( perp(X1175,X1176,X1177,X1178)
| ~ perpAt(X1175,X1176,X1179,X1177,X1178) ) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X12,X15,X13,X16] :
( ~ perp(X12,X15,X13,X16)
| perp(X13,X16,X12,X15) ),
inference(fof_simplification,[status(thm)],[aSatz8_12b]) ).
fof(c_0_23,plain,
! [X943,X944,X945,X946,X947] :
( X943 = X944
| X945 = X946
| ~ s_col(X945,X946,X943)
| ~ s_col(X945,X946,X944)
| ~ s_col(X945,X946,X947)
| s_col(X943,X944,X947) ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
! [X763,X764,X765] :
( ~ s_col(X763,X764,X765)
| s_col(X765,X764,X763) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X772,X773] : s_col(X772,X772,X773),
inference(variable_rename,[status(thm)],[aSatz4_12]) ).
fof(c_0_26,plain,
! [X2,X3,X1,X9,X10,X35,X4] :
( ( ~ perpAt(X2,X3,X1,X9,X10)
| s_col(X2,X3,X1) )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| s_col(X9,X10,X1) )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| X2 != X3 )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| X9 != X10 )
& ( ~ perpAt(X2,X3,X1,X9,X10)
| ~ s_col(X2,X3,X35)
| ~ s_col(X9,X10,X4)
| s_r(X35,X1,X4) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| s_col(X2,X3,f811(X2,X3,X9,X10,X1)) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| s_col(X9,X10,g811(X2,X3,X9,X10,X1)) )
& ( perpAt(X2,X3,X1,X9,X10)
| X2 = X3
| X9 = X10
| ~ s_col(X2,X3,X1)
| ~ s_col(X9,X10,X1)
| ~ s_r(f811(X2,X3,X9,X10,X1),X1,g811(X2,X3,X9,X10,X1)) ) ),
inference(fof_simplification,[status(thm)],[d_Defn8_11a]) ).
cnf(c_0_27,plain,
( X1 = X2
| X3 = X1
| s_col(X1,X3,X4)
| ~ s_col(X1,X2,X3)
| ~ s_col(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
s_col(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( s_col(X4,X5,X3)
| ~ perpAt(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( perpAt(X1,X2,il(X1,X2,X3,X4),X3,X4)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,plain,
! [X1090,X1091,X1092,X1093] :
( ~ perp(X1090,X1091,X1092,X1093)
| perp(X1092,X1093,X1090,X1091) ),
inference(variable_rename,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( X1 = X2
| X3 = X4
| s_col(X1,X2,X5)
| ~ s_col(X3,X4,X1)
| ~ s_col(X3,X4,X2)
| ~ s_col(X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( s_col(X3,X2,X1)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
s_col(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,negated_conjecture,
s_col(esk1_0,esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_36,plain,
! [X12,X15,X14] :
( ~ s_r(X12,X15,X14)
| ~ s_col(X12,X15,X14)
| X12 = X15
| X14 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz8_9]) ).
fof(c_0_37,plain,
! [X1168,X1169,X1170,X1171,X1172,X1173,X1174] :
( ( ~ perpAt(X1168,X1169,X1170,X1171,X1172)
| s_col(X1168,X1169,X1170) )
& ( ~ perpAt(X1168,X1169,X1170,X1171,X1172)
| s_col(X1171,X1172,X1170) )
& ( ~ perpAt(X1168,X1169,X1170,X1171,X1172)
| X1168 != X1169 )
& ( ~ perpAt(X1168,X1169,X1170,X1171,X1172)
| X1171 != X1172 )
& ( ~ perpAt(X1168,X1169,X1170,X1171,X1172)
| ~ s_col(X1168,X1169,X1173)
| ~ s_col(X1171,X1172,X1174)
| s_r(X1173,X1170,X1174) )
& ( perpAt(X1168,X1169,X1170,X1171,X1172)
| X1168 = X1169
| X1171 = X1172
| ~ s_col(X1168,X1169,X1170)
| ~ s_col(X1171,X1172,X1170)
| s_col(X1168,X1169,f811(X1168,X1169,X1171,X1172,X1170)) )
& ( perpAt(X1168,X1169,X1170,X1171,X1172)
| X1168 = X1169
| X1171 = X1172
| ~ s_col(X1168,X1169,X1170)
| ~ s_col(X1171,X1172,X1170)
| s_col(X1171,X1172,g811(X1168,X1169,X1171,X1172,X1170)) )
& ( perpAt(X1168,X1169,X1170,X1171,X1172)
| X1168 = X1169
| X1171 = X1172
| ~ s_col(X1168,X1169,X1170)
| ~ s_col(X1171,X1172,X1170)
| ~ s_r(f811(X1168,X1169,X1171,X1172,X1170),X1170,g811(X1168,X1169,X1171,X1172,X1170)) ) ),
inference(variable_rename,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( esk2_0 = esk1_0
| esk1_0 = X1
| s_col(esk1_0,X1,esk3_0)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_39,plain,
( s_col(X1,X2,il(X3,X4,X1,X2))
| ~ perp(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
perp(esk1_0,esk2_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,negated_conjecture,
( esk2_0 = esk1_0
| X1 = X2
| s_col(X1,X2,esk3_0)
| ~ s_col(esk1_0,esk2_0,X2)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_43,plain,
s_col(X1,X2,X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,negated_conjecture,
( esk2_0 = esk1_0
| esk1_0 = X1
| s_col(esk1_0,X1,esk4_0)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
fof(c_0_45,plain,
! [X1076,X1077,X1078] :
( ~ s_r(X1076,X1077,X1078)
| ~ s_col(X1076,X1077,X1078)
| X1076 = X1077
| X1078 = X1077 ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( s_r(X6,X3,X7)
| ~ perpAt(X1,X2,X3,X4,X5)
| ~ s_col(X1,X2,X6)
| ~ s_col(X4,X5,X7) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( il(X1,X2,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk1_0,il(X1,X2,esk1_0,esk2_0),esk3_0)
| ~ perp(X1,X2,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
perp(esk3_0,esk4_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_49,plain,
! [X12,X15,X14] :
( ~ s_col(X12,X15,X14)
| s_col(X14,X12,X15) ),
inference(fof_simplification,[status(thm)],[aSatz4_11b]) ).
cnf(c_0_50,negated_conjecture,
( esk2_0 = esk1_0
| X1 = esk2_0
| s_col(X1,esk2_0,esk3_0)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( il(X1,X2,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk1_0,il(X1,X2,esk1_0,esk2_0),esk4_0)
| ~ perp(X1,X2,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_52,plain,
( X1 = X2
| X3 = X2
| ~ s_r(X1,X2,X3)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
( s_r(X1,il(X2,X3,X4,X5),X6)
| ~ perp(X2,X3,X4,X5)
| ~ s_col(X4,X5,X6)
| ~ s_col(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_54,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk1_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_55,plain,
! [X774,X775] : s_col(X774,X775,X774),
inference(variable_rename,[status(thm)],[aSatz4_12b]) ).
fof(c_0_56,plain,
! [X760,X761,X762] :
( ~ s_col(X760,X761,X762)
| s_col(X762,X760,X761) ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( il(X1,X2,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(il(X1,X2,esk1_0,esk2_0),esk2_0,esk3_0)
| ~ perp(X1,X2,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_58,negated_conjecture,
( esk2_0 = esk1_0
| X1 = X2
| s_col(X1,X2,esk4_0)
| ~ s_col(esk1_0,esk2_0,X2)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_59,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk1_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_60,plain,
( X1 = il(X2,X3,X4,X5)
| il(X2,X3,X4,X5) = X6
| ~ perp(X2,X3,X4,X5)
| ~ s_col(X1,il(X2,X3,X4,X5),X6)
| ~ s_col(X4,X5,X6)
| ~ s_col(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk3_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_54]) ).
cnf(c_0_62,plain,
s_col(X1,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( s_col(X3,X1,X2)
| ~ s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(il(esk3_0,esk4_0,esk1_0,esk2_0),esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_65,negated_conjecture,
( esk2_0 = esk1_0
| X1 = esk2_0
| s_col(X1,esk2_0,esk4_0)
| ~ s_col(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_66,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| s_col(esk4_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| il(esk3_0,esk4_0,esk1_0,esk2_0) = esk3_0
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_48]),c_0_62]),c_0_62])]) ).
cnf(c_0_68,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(esk3_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( il(X1,X2,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(il(X1,X2,esk1_0,esk2_0),esk2_0,esk4_0)
| ~ perp(X1,X2,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_39]) ).
cnf(c_0_70,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| il(esk3_0,esk4_0,esk1_0,esk2_0) = esk4_0
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_66]),c_0_48]),c_0_62]),c_0_43])]) ).
cnf(c_0_71,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| esk3_0 != esk1_0 ),
inference(ef,[status(thm)],[c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| il(esk3_0,esk4_0,esk1_0,esk2_0) = esk3_0
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_48]),c_0_43]),c_0_62])]) ).
cnf(c_0_73,plain,
( ~ perpAt(X1,X2,X3,X4,X5)
| X4 != X5 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_74,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(il(esk3_0,esk4_0,esk1_0,esk2_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_48]) ).
cnf(c_0_75,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_67]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_77,plain,
~ perpAt(X1,X2,X3,X4,X4),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| s_col(esk4_0,il(esk3_0,esk4_0,esk1_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( esk3_0 = esk1_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
~ perp(X1,X2,X3,X3),
inference(spm,[status(thm)],[c_0_77,c_0_30]) ).
cnf(c_0_81,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| il(esk3_0,esk4_0,esk1_0,esk2_0) = esk4_0
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_78]),c_0_48]),c_0_43]),c_0_43])]) ).
cnf(c_0_82,negated_conjecture,
( esk2_0 = esk1_0
| esk3_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_79]),c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( il(esk3_0,esk4_0,esk1_0,esk2_0) = esk2_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0
| esk4_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( il(esk1_0,esk4_0,esk1_0,esk2_0) = esk1_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( esk2_0 = esk1_0
| perp(esk1_0,esk4_0,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( esk4_0 = esk1_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_75,c_0_83]) ).
cnf(c_0_87,plain,
( ~ perpAt(X1,X2,X3,X4,X5)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_88,negated_conjecture,
( esk2_0 = esk1_0
| perpAt(esk1_0,esk4_0,esk1_0,esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_84]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( esk2_0 = esk1_0
| esk4_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_86]),c_0_80]) ).
cnf(c_0_90,plain,
~ perpAt(X1,X1,X2,X3,X4),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_91]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO507+1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:59:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 219.01/146.46 % Version : CSE_E---1.7
% 219.01/146.46 % Problem : theBenchmark.p
% 219.01/146.46 % SZS status Theorem for theBenchmark.p
% 219.01/146.46 % SZS output start CNFRefutation
% See solution above
% 219.62/147.07 % Total time : 124.402s
%------------------------------------------------------------------------------