%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO528+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 : n001.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 12:28:24 PM UTC 2026
% Result : Theorem 14.64s 2.82s
% Output : CNFRefutation 14.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 123 ( 42 unt; 0 def)
% Number of atoms : 340 ( 91 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 357 ( 140 ~; 185 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 301 ( 3 sgn 209 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz10_14,conjecture,
! [X12,X15,X13,X37] :
( opposite(X13,X12,X15,X37)
| s_col(X12,X15,X13)
| reflect(X12,X15,X13) != X37
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_14) ).
fof(aSatz10_8b,axiom,
! [X12,X15,X13] :
( reflect(X12,X15,X13) = X13
| ~ s_col(X12,X15,X13)
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8b) ).
fof(aSatz10_10,axiom,
! [X12,X15,X13,X16] :
( s_e(X13,X16,reflect(X12,X15,X13),reflect(X12,X15,X16))
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_10) ).
fof(aSatz4_12b,axiom,
! [X12,X15] : s_col(X12,X15,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_12b) ).
fof(aSatz7_18,axiom,
! [X12,X13,X15] :
( X12 = X15
| s(X12,X13) != s(X15,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_18) ).
fof(aSatz7_6,axiom,
! [X13,X12,X16] :
( X16 = s(X12,X13)
| ~ s_m(X13,X12,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).
fof(aSatz7_25,axiom,
! [X14,X12,X15] :
( s_m(X12,isomidpoint(X12,X15,X14),X15)
| ~ s_e(X14,X12,X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_25) ).
fof(aSatz7_7,axiom,
! [X12,X13] : s(X12,s(X12,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).
fof(aSatz8_22,axiom,
! [X12,X15] : s_m(X12,midpoint(X12,X15),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
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(aSatz3_3,axiom,
! [X20,X21] : s_t(X20,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_3) ).
fof(aSatz7_17,axiom,
! [X13,X12,X16,X15] :
( X12 = X15
| ~ s_m(X13,X15,X16)
| ~ s_m(X13,X12,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_17) ).
fof(aSatz2_2,axiom,
! [X12,X15,X14,X17] :
( s_e(X14,X17,X12,X15)
| ~ s_e(X12,X15,X14,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).
fof(aSatz10_8a,axiom,
! [X12,X15,X13] :
( s_col(X12,X15,X13)
| reflect(X12,X15,X13) != X13
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_8a) ).
fof(aSatz4_18,axiom,
! [X12,X15,X14,X22] :
( X14 = X22
| ~ s_e(X15,X14,X15,X22)
| ~ s_e(X12,X14,X12,X22)
| ~ s_col(X12,X15,X14)
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz4_18) ).
fof(d_Defn7_1,axiom,
! [X12,X29,X15] :
( ( s_m(X12,X29,X15)
| ~ s_e(X29,X12,X29,X15)
| ~ s_t(X12,X29,X15) )
& ( s_e(X29,X12,X29,X15)
| ~ s_m(X12,X29,X15) )
& ( s_t(X12,X29,X15)
| ~ s_m(X12,X29,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn7_1) ).
fof(d_Defn9_1,axiom,
! [X13,X16,X12,X15,X36] :
( ( s_col(X13,X16,il(X12,X15,X13,X16))
| ~ opposite(X12,X13,X16,X15) )
& ( s_t(X12,il(X12,X15,X13,X16),X15)
| ~ opposite(X12,X13,X16,X15) )
& ( ~ s_col(X13,X16,X15)
| ~ opposite(X12,X13,X16,X15) )
& ( ~ s_col(X13,X16,X12)
| ~ opposite(X12,X13,X16,X15) )
& ( opposite(X12,X13,X16,X15)
| ~ s_col(X13,X16,X36)
| ~ s_t(X12,X36,X15)
| s_col(X13,X16,X15)
| s_col(X13,X16,X12)
| X13 = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_1) ).
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(aSatz10_2a,axiom,
! [X12,X15,X13] :
( ( perp(X12,X15,X13,reflect(X12,X15,X13))
| X13 = reflect(X12,X15,X13)
| X12 = X15 )
& ( s_col(X12,X15,midpoint(X13,reflect(X12,X15,X13)))
| X12 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2a) ).
fof(aLemma9_13a,axiom,
! [X13,X16,X12,X15] :
( samesideline(X13,X16,X15,X12)
| ~ samesideline(X13,X16,X12,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13a) ).
fof(aLemma9_13f,axiom,
! [X13,X16,X27,X28] :
( opposite(X27,X13,X16,X28)
| samesideline(X27,X28,X13,X16)
| s_col(X13,X16,X28)
| s_col(X13,X16,X27)
| X13 = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13f) ).
fof(aLemma9_13d,axiom,
! [X12,X15,X13,X16] :
( samesideline(X16,X13,X12,X15)
| ~ samesideline(X13,X16,X12,X15)
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLemma9_13d) ).
fof(aSatz9_9,axiom,
! [X12,X13,X16,X15] :
( ~ samesideline(X12,X15,X13,X16)
| ~ opposite(X12,X13,X16,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_9) ).
fof(c_0_23,negated_conjecture,
~ ! [X12,X15,X13,X37] :
( opposite(X13,X12,X15,X37)
| s_col(X12,X15,X13)
| reflect(X12,X15,X13) != X37
| X12 = X15 ),
inference(assume_negation,[status(cth)],[aSatz10_14]) ).
fof(c_0_24,negated_conjecture,
~ ! [X12,X15,X13,X37] :
( opposite(X13,X12,X15,X37)
| s_col(X12,X15,X13)
| reflect(X12,X15,X13) != X37
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_25,plain,
! [X12,X15,X13] :
( reflect(X12,X15,X13) = X13
| ~ s_col(X12,X15,X13)
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz10_8b]) ).
fof(c_0_26,plain,
! [X837,X838,X839,X840] :
( s_e(X839,X840,reflect(X837,X838,X839),reflect(X837,X838,X840))
| X837 = X838 ),
inference(variable_rename,[status(thm)],[aSatz10_10]) ).
fof(c_0_27,negated_conjecture,
( ~ opposite(esk3_0,esk1_0,esk2_0,esk4_0)
& ~ s_col(esk1_0,esk2_0,esk3_0)
& reflect(esk1_0,esk2_0,esk3_0) = esk4_0
& esk1_0 != esk2_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_28,plain,
! [X830,X831,X832] :
( reflect(X830,X831,X832) = X832
| ~ s_col(X830,X831,X832)
| X830 = X831 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_25])]) ).
fof(c_0_29,plain,
! [X209,X210] : s_col(X209,X210,X209),
inference(variable_rename,[status(thm)],[aSatz4_12b]) ).
fof(c_0_30,plain,
! [X12,X13,X15] :
( X12 = X15
| s(X12,X13) != s(X15,X13) ),
inference(fof_simplification,[status(thm)],[aSatz7_18]) ).
fof(c_0_31,plain,
! [X13,X12,X16] :
( X16 = s(X12,X13)
| ~ s_m(X13,X12,X16) ),
inference(fof_simplification,[status(thm)],[aSatz7_6]) ).
fof(c_0_32,plain,
! [X14,X12,X15] :
( s_m(X12,isomidpoint(X12,X15,X14),X15)
| ~ s_e(X14,X12,X14,X15) ),
inference(fof_simplification,[status(thm)],[aSatz7_25]) ).
cnf(c_0_33,plain,
( s_e(X3,X4,reflect(X1,X2,X3),reflect(X1,X2,X4))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
reflect(esk1_0,esk2_0,esk3_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( ~ s_col(X1,X2,X3)
| reflect(X1,X2,X3) = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
s_col(X1,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,plain,
! [X452,X453,X454] :
( X452 = X454
| s(X452,X453) != s(X454,X453) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_39,plain,
! [X414,X415] : s(X414,s(X414,X415)) = X415,
inference(variable_rename,[status(thm)],[aSatz7_7]) ).
fof(c_0_40,plain,
! [X411,X412,X413] :
( X413 = s(X412,X411)
| ~ s_m(X411,X412,X413) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_41,plain,
! [X605,X606] : s_m(X605,midpoint(X605,X606),X606),
inference(variable_rename,[status(thm)],[aSatz8_22]) ).
fof(c_0_42,plain,
! [X487,X488,X489] :
( s_m(X488,isomidpoint(X488,X489,X487),X489)
| ~ s_e(X487,X488,X487,X489) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).
cnf(c_0_43,negated_conjecture,
s_e(X1,esk3_0,reflect(esk1_0,esk2_0,X1),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_44,plain,
( X1 = X2
| reflect(X1,X2,X1) = X1 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_45,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]) ).
cnf(c_0_46,plain,
( s(X1,X2) != s(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
s(X1,s(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( ~ s_m(X1,X2,X3)
| X3 = s(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
s_m(X1,midpoint(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( ~ s_e(X1,X2,X1,X3)
| s_m(X2,isomidpoint(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,negated_conjecture,
s_e(esk1_0,esk3_0,esk1_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_35]) ).
fof(c_0_52,plain,
! [X891,X892,X893] :
( ( ~ s_t(X893,X891,X892)
| s_col(X891,X892,X893) )
& ( ~ s_t(X892,X893,X891)
| s_col(X891,X892,X893) )
& ( ~ s_t(X891,X892,X893)
| s_col(X891,X892,X893) )
& ( s_t(X893,X891,X892)
| s_t(X892,X893,X891)
| s_t(X891,X892,X893)
| ~ s_col(X891,X892,X893) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
fof(c_0_53,plain,
! [X128,X129] : s_t(X128,X128,X129),
inference(variable_rename,[status(thm)],[aSatz3_3]) ).
cnf(c_0_54,plain,
( s(X1,s(X2,X3)) != X3
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
s(midpoint(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
s_m(esk3_0,isomidpoint(esk3_0,esk4_0,esk1_0),esk4_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( ~ s_t(X2,X3,X1)
| s_col(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
s_t(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_59,plain,
! [X13,X12,X16,X15] :
( X12 = X15
| ~ s_m(X13,X15,X16)
| ~ s_m(X13,X12,X16) ),
inference(fof_simplification,[status(thm)],[aSatz7_17]) ).
cnf(c_0_60,plain,
midpoint(s(X1,X2),X2) = X1,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_61,negated_conjecture,
s(isomidpoint(esk3_0,esk4_0,esk1_0),esk3_0) = esk4_0,
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
fof(c_0_62,plain,
! [X12,X15,X14,X17] :
( s_e(X14,X17,X12,X15)
| ~ s_e(X12,X15,X14,X17) ),
inference(fof_simplification,[status(thm)],[aSatz2_2]) ).
cnf(c_0_63,plain,
s_col(X1,X2,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_64,plain,
! [X12,X15,X13] :
( s_col(X12,X15,X13)
| reflect(X12,X15,X13) != X13
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz10_8a]) ).
fof(c_0_65,plain,
! [X448,X449,X450,X451] :
( X449 = X451
| ~ s_m(X448,X451,X450)
| ~ s_m(X448,X449,X450) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
isomidpoint(esk3_0,esk4_0,esk1_0) = midpoint(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_67,plain,
! [X12,X15,X14,X22] :
( X14 = X22
| ~ s_e(X15,X14,X15,X22)
| ~ s_e(X12,X14,X12,X22)
| ~ s_col(X12,X15,X14)
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz4_18]) ).
fof(c_0_68,plain,
! [X79,X80,X81,X82] :
( s_e(X81,X82,X79,X80)
| ~ s_e(X79,X80,X81,X82) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_62])]) ).
cnf(c_0_69,plain,
( X1 = X2
| reflect(X1,X2,X2) = X2 ),
inference(spm,[status(thm)],[c_0_36,c_0_63]) ).
fof(c_0_70,plain,
! [X827,X828,X829] :
( s_col(X827,X828,X829)
| reflect(X827,X828,X829) != X829
| X827 = X828 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
cnf(c_0_71,plain,
( ~ s_m(X1,X4,X3)
| ~ s_m(X1,X2,X3)
| X2 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,negated_conjecture,
s_m(esk3_0,midpoint(esk4_0,esk3_0),esk4_0),
inference(rw,[status(thm)],[c_0_56,c_0_66]) ).
fof(c_0_73,plain,
! [X235,X236,X237,X238] :
( X237 = X238
| ~ s_e(X236,X237,X236,X238)
| ~ s_e(X235,X237,X235,X238)
| ~ s_col(X235,X236,X237)
| X235 = X236 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_67])]) ).
cnf(c_0_74,plain,
( ~ s_e(X1,X2,X3,X4)
| s_e(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,negated_conjecture,
s_e(esk2_0,esk3_0,esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_35]) ).
cnf(c_0_76,plain,
( reflect(X1,X2,X3) != X3
| s_col(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
~ s_col(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_78,plain,
! [X12,X29,X15] :
( ( s_m(X12,X29,X15)
| ~ s_e(X29,X12,X29,X15)
| ~ s_t(X12,X29,X15) )
& ( s_e(X29,X12,X29,X15)
| ~ s_m(X12,X29,X15) )
& ( s_t(X12,X29,X15)
| ~ s_m(X12,X29,X15) ) ),
inference(fof_simplification,[status(thm)],[d_Defn7_1]) ).
cnf(c_0_79,negated_conjecture,
( ~ s_m(esk3_0,X1,esk4_0)
| X1 = midpoint(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
( ~ s_e(X2,X3,X2,X4)
| ~ s_e(X1,X3,X1,X4)
| ~ s_col(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,negated_conjecture,
s_e(esk2_0,esk4_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
esk4_0 != esk3_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_34]),c_0_35]),c_0_77]) ).
fof(c_0_83,plain,
! [X13,X16,X12,X15,X36] :
( ( s_col(X13,X16,il(X12,X15,X13,X16))
| ~ opposite(X12,X13,X16,X15) )
& ( s_t(X12,il(X12,X15,X13,X16),X15)
| ~ opposite(X12,X13,X16,X15) )
& ( ~ s_col(X13,X16,X15)
| ~ opposite(X12,X13,X16,X15) )
& ( ~ s_col(X13,X16,X12)
| ~ opposite(X12,X13,X16,X15) )
& ( opposite(X12,X13,X16,X15)
| ~ s_col(X13,X16,X36)
| ~ s_t(X12,X36,X15)
| s_col(X13,X16,X15)
| s_col(X13,X16,X12)
| X13 = X16 ) ),
inference(fof_simplification,[status(thm)],[d_Defn9_1]) ).
fof(c_0_84,plain,
! [X910,X911,X912] :
( ( s_m(X910,X911,X912)
| ~ s_e(X911,X910,X911,X912)
| ~ s_t(X910,X911,X912) )
& ( s_e(X911,X910,X911,X912)
| ~ s_m(X910,X911,X912) )
& ( s_t(X910,X911,X912)
| ~ s_m(X910,X911,X912) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_78])]) ).
cnf(c_0_85,negated_conjecture,
midpoint(esk4_0,esk3_0) = midpoint(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_79,c_0_49]) ).
fof(c_0_86,plain,
! [X12,X15,X14] :
( s_col(X15,X12,X14)
| ~ s_col(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz4_11d]) ).
fof(c_0_87,plain,
! [X805,X806,X807] :
( ( perp(X805,X806,X807,reflect(X805,X806,X807))
| X807 = reflect(X805,X806,X807)
| X805 = X806 )
& ( s_col(X805,X806,midpoint(X807,reflect(X805,X806,X807)))
| X805 = X806 ) ),
inference(variable_rename,[status(thm)],[aSatz10_2a]) ).
fof(c_0_88,plain,
! [X13,X16,X12,X15] :
( samesideline(X13,X16,X15,X12)
| ~ samesideline(X13,X16,X12,X15) ),
inference(fof_simplification,[status(thm)],[aLemma9_13a]) ).
fof(c_0_89,plain,
! [X791,X792,X793,X794] :
( opposite(X793,X791,X792,X794)
| samesideline(X793,X794,X791,X792)
| s_col(X791,X792,X794)
| s_col(X791,X792,X793)
| X791 = X792 ),
inference(variable_rename,[status(thm)],[aLemma9_13f]) ).
cnf(c_0_90,negated_conjecture,
( ~ s_e(X1,esk4_0,X1,esk3_0)
| ~ s_col(X1,esk2_0,esk4_0)
| X1 = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_91,negated_conjecture,
s_e(esk1_0,esk4_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_74,c_0_51]) ).
fof(c_0_92,plain,
! [X935,X936,X937,X938,X939] :
( ( s_col(X935,X936,il(X937,X938,X935,X936))
| ~ opposite(X937,X935,X936,X938) )
& ( s_t(X937,il(X937,X938,X935,X936),X938)
| ~ opposite(X937,X935,X936,X938) )
& ( ~ s_col(X935,X936,X938)
| ~ opposite(X937,X935,X936,X938) )
& ( ~ s_col(X935,X936,X937)
| ~ opposite(X937,X935,X936,X938) )
& ( opposite(X937,X935,X936,X938)
| ~ s_col(X935,X936,X939)
| ~ s_t(X937,X939,X938)
| s_col(X935,X936,X938)
| s_col(X935,X936,X937)
| X935 = X936 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_83])]) ).
cnf(c_0_93,plain,
( ~ s_m(X1,X2,X3)
| s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_94,negated_conjecture,
s_m(esk4_0,midpoint(esk3_0,esk4_0),esk3_0),
inference(spm,[status(thm)],[c_0_49,c_0_85]) ).
fof(c_0_95,plain,
! [X201,X202,X203] :
( s_col(X202,X201,X203)
| ~ s_col(X201,X202,X203) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_86])]) ).
cnf(c_0_96,plain,
( s_col(X1,X2,midpoint(X3,reflect(X1,X2,X3)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_97,plain,
! [X12,X15,X13,X16] :
( samesideline(X16,X13,X12,X15)
| ~ samesideline(X13,X16,X12,X15)
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aLemma9_13d]) ).
fof(c_0_98,plain,
! [X755,X756,X757,X758] :
( samesideline(X755,X756,X758,X757)
| ~ samesideline(X755,X756,X757,X758) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_88])]) ).
cnf(c_0_99,negated_conjecture,
~ opposite(esk3_0,esk1_0,esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_100,plain,
( opposite(X3,X1,X2,X4)
| samesideline(X3,X4,X1,X2)
| s_col(X1,X2,X4)
| s_col(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_101,negated_conjecture,
~ s_col(esk1_0,esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_35]) ).
fof(c_0_102,plain,
! [X12,X13,X16,X15] :
( ~ samesideline(X12,X15,X13,X16)
| ~ opposite(X12,X13,X16,X15) ),
inference(fof_simplification,[status(thm)],[aSatz9_9]) ).
cnf(c_0_103,plain,
( ~ s_col(X1,X2,X5)
| ~ s_t(X3,X5,X4)
| opposite(X3,X1,X2,X4)
| s_col(X1,X2,X4)
| s_col(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_104,negated_conjecture,
s_t(esk4_0,midpoint(esk3_0,esk4_0),esk3_0),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_105,plain,
( ~ s_col(X1,X2,X3)
| s_col(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,negated_conjecture,
s_col(esk1_0,esk2_0,midpoint(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_34]),c_0_35]) ).
cnf(c_0_107,negated_conjecture,
( ~ s_e(X1,esk4_0,X1,esk3_0)
| ~ s_col(X1,esk1_0,esk4_0)
| X1 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_91]),c_0_82]) ).
cnf(c_0_108,negated_conjecture,
( ~ s_e(X1,esk3_0,X1,esk4_0)
| ~ s_col(X1,esk1_0,esk3_0)
| X1 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_51]),c_0_82]) ).
fof(c_0_109,plain,
! [X769,X770,X771,X772] :
( samesideline(X772,X771,X769,X770)
| ~ samesideline(X771,X772,X769,X770)
| X769 = X770 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_97])]) ).
cnf(c_0_110,plain,
( ~ samesideline(X1,X2,X3,X4)
| samesideline(X1,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_111,negated_conjecture,
samesideline(esk3_0,esk4_0,esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_35]),c_0_101]),c_0_77]) ).
fof(c_0_112,plain,
! [X746,X747,X748,X749] :
( ~ samesideline(X746,X749,X747,X748)
| ~ opposite(X746,X747,X748,X749) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_102])]) ).
cnf(c_0_113,negated_conjecture,
( ~ s_col(X1,X2,midpoint(esk3_0,esk4_0))
| s_col(X1,X2,esk3_0)
| s_col(X1,X2,esk4_0)
| opposite(esk4_0,X1,X2,esk3_0)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_114,negated_conjecture,
s_col(esk2_0,esk1_0,midpoint(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_115,negated_conjecture,
~ s_col(esk2_0,esk1_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_81]),c_0_35]) ).
cnf(c_0_116,negated_conjecture,
~ s_col(esk2_0,esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_75]),c_0_35]) ).
cnf(c_0_117,plain,
( ~ samesideline(X3,X4,X1,X2)
| samesideline(X4,X3,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_118,negated_conjecture,
samesideline(esk3_0,esk4_0,esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,plain,
( ~ samesideline(X1,X4,X2,X3)
| ~ opposite(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_120,negated_conjecture,
opposite(esk4_0,esk2_0,esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_35]),c_0_115]),c_0_116]) ).
cnf(c_0_121,negated_conjecture,
samesideline(esk4_0,esk3_0,esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_35]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.58 % Computer : n001.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Sun Sep 20 17:23:15 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 Running first-order theorem proving
% 0.12/0.62 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
% 14.64/2.82 % Version: 3.5.1
% 14.64/2.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.64/2.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.64/2.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.64/2.82 % Starting new_bool_3 with 300s (1) cores
% 14.64/2.82 % Starting new_bool_1 with 300s (1) cores
% 14.64/2.82 % Starting sh5l with 300s (1) cores
% 14.64/2.82 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1056958 completed with status 0
% 14.64/2.82 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 14.64/2.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.64/2.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.64/2.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.64/2.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.64/2.82 % No SInE strategy applied
% 14.64/2.82 % Search class: FGHSM-FSLF33-MFFFFFNN
% 14.64/2.82 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 14.64/2.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.64/2.82 % Starting SubtermCWHack with 136s (1) cores
% 14.64/2.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 14.64/2.82 % Starting new_bool_3 with 393s (1) cores
% 14.64/2.82 % Starting G-E--_303_C18_F1_URBAN_S0Y with 330s (1) cores
% 14.64/2.82 % Starting Y1006__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 14.64/2.82 % new_bool_3 with pid 1056967 completed with status 0
% 14.64/2.82 % Result found by new_bool_3
% 14.64/2.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.64/2.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.64/2.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.64/2.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.64/2.82 % No SInE strategy applied
% 14.64/2.82 % Search class: FGHSM-FSLF33-MFFFFFNN
% 14.64/2.82 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 14.64/2.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.64/2.82 % Starting SubtermCWHack with 136s (1) cores
% 14.64/2.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 14.64/2.82 % Starting new_bool_3 with 393s (1) cores
% 14.64/2.82 % Preprocessing time : 0.004 s
% 14.64/2.82 % Presaturation interreduction done
% 14.64/2.82
% 14.64/2.82 % Proof found!
% 14.64/2.82 % SZS status Theorem
% 14.64/2.82 % SZS output start CNFRefutation
% See solution above
% 14.64/2.82 % Parsed axioms : 213
% 14.64/2.82 % Removed by relevancy pruning/SinE : 0
% 14.64/2.82 % Initial clauses : 307
% 14.64/2.82 % Removed in clause preprocessing : 1
% 14.64/2.82 % Initial clauses in saturation : 306
% 14.64/2.82 % Processed clauses : 13746
% 14.64/2.82 % ...of these trivial : 3678
% 14.64/2.82 % ...subsumed : 4081
% 14.64/2.82 % ...remaining for further processing : 5987
% 14.64/2.82 % Other redundant clauses eliminated : 67
% 14.64/2.82 % Clauses deleted for lack of memory : 0
% 14.64/2.82 % Backward-subsumed : 32
% 14.64/2.82 % Backward-rewritten : 599
% 14.64/2.82 % Generated clauses : 137761
% 14.64/2.82 % ...of the previous two non-redundant : 114923
% 14.64/2.82 % ...aggressively subsumed : 0
% 14.64/2.82 % Contextual simplify-reflections : 22
% 14.64/2.82 % Paramodulations : 137688
% 14.64/2.82 % Factorizations : 2
% 14.64/2.82 % NegExts : 0
% 14.64/2.82 % Equation resolutions : 71
% 14.64/2.82 % Disequality decompositions : 0
% 14.64/2.82 % Total rewrite steps : 38278
% 14.64/2.82 % ...of those cached : 35022
% 14.64/2.82 % Propositional unsat checks : 1
% 14.64/2.82 % Propositional check models : 0
% 14.64/2.82 % Propositional check unsatisfiable : 0
% 14.64/2.82 % Propositional clauses : 0
% 14.64/2.82 % Propositional clauses after purity: 0
% 14.64/2.82 % Propositional unsat core size : 0
% 14.64/2.82 % Propositional preprocessing time : 0.000
% 14.64/2.82 % Propositional encoding time : 0.068
% 14.64/2.82 % Propositional solver time : 0.095
% 14.64/2.82 % Success case prop preproc time : 0.000
% 14.64/2.82 % Success case prop encoding time : 0.000
% 14.64/2.82 % Success case prop solver time : 0.000
% 14.64/2.82 % Current number of processed clauses : 5062
% 14.64/2.82 % Positive orientable unit clauses : 1685
% 14.64/2.82 % Positive unorientable unit clauses: 1
% 14.64/2.82 % Negative unit clauses : 77
% 14.64/2.82 % Non-unit-clauses : 3299
% 14.64/2.82 % Current number of unprocessed clauses: 101081
% 14.64/2.82 % ...number of literals in the above : 256534
% 14.64/2.82 % Current number of archived formulas : 0
% 14.64/2.82 % Current number of archived clauses : 907
% 14.64/2.82 % Clause-clause subsumption calls (NU) : 1571425
% 14.64/2.82 % Rec. Clause-clause subsumption calls : 1161832
% 14.64/2.82 % Non-unit clause-clause subsumptions : 3806
% 14.64/2.82 % Unit Clause-clause subsumption calls : 67355
% 14.64/2.82 % Rewrite failures with RHS unbound : 0
% 14.64/2.82 % BW rewrite match attempts : 20054
% 14.64/2.82 % BW rewrite match successes : 94
% 14.64/2.82 % Condensation attempts : 0
% 14.64/2.82 % Condensation successes : 0
% 14.64/2.82 % Termbank termtop insertions : 2657131
% 14.64/2.82 % Search garbage collected termcells : 2650
% 14.64/2.82
% 14.64/2.82 % -------------------------------------------------
% 14.64/2.82 % User time : 1.997 s
% 14.64/2.82 % System time : 0.111 s
% 14.64/2.82 % Total time : 2.108 s
% 14.64/2.82 % Maximum resident set size: 5304 pages
% 14.64/2.82
% 14.64/2.82 % -------------------------------------------------
% 14.64/2.82 % User time : 9.857 s
% 14.64/2.82 % System time : 0.316 s
% 14.64/2.82 % Total time : 10.174 s
% 14.64/2.82 % Maximum resident set size: 4864 pages
% 14.64/2.82 % E exiting
%------------------------------------------------------------------------------