%------------------------------------------------------------------------------
% File : E-SAT---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 : n012.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 12:30:19 PM UTC 2026
% Result : Theorem 9.43s 1.60s
% Output : CNFRefutation 9.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 106 ( 23 unt; 0 def)
% Number of atoms : 409 ( 140 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 503 ( 200 ~; 244 |; 59 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 301 ( 2 sgn 201 !; 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_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(aSatz10_5,axiom,
! [X12,X15,X13] :
( reflect(X12,X15,reflect(X12,X15,X13)) = X13
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_5) ).
fof(aExtPerp4,axiom,
! [X12,X15,X13,X16] :
( perp(X12,X15,X16,X13)
| ~ perp(X12,X15,X13,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aExtPerp4) ).
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(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(aperp1,axiom,
! [X12,X15,X13,X16] :
( perp(X15,X12,X13,X16)
| ~ perp(X12,X15,X13,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aperp1) ).
fof(aSatz10_6,axiom,
! [X12,X15,X13,X37] :
( X13 = reflect(X12,X15,X37)
| reflect(X12,X15,X13) != X37
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_6) ).
fof(aSatz10_7,axiom,
! [X12,X15,X13,X16] :
( X13 = X16
| reflect(X12,X15,X13) != reflect(X12,X15,X16)
| X12 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_7) ).
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_2b,axiom,
! [X12,X15,X13,X37] :
( ( X37 = reflect(X12,X15,X13)
| X13 != X37
| ~ s_col(X12,X15,midpoint(X13,X37))
| X12 = X15 )
& ( X37 = reflect(X12,X15,X13)
| ~ perp(X12,X15,X13,X37)
| ~ s_col(X12,X15,midpoint(X13,X37))
| X12 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz10_2b) ).
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(aA6,axiom,
! [X1,X2] :
( X1 = X2
| ~ s_t(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA6) ).
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(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(aSatz9_8,axiom,
! [X12,X13,X16,X14,X15] :
( ~ samesideline(X12,X15,X13,X16)
| opposite(X15,X13,X16,X14)
| ~ opposite(X12,X13,X16,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz9_8) ).
fof(aSatz8_22,axiom,
! [X12,X15] : s_m(X12,midpoint(X12,X15),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz8_22) ).
fof(d_Defn9_7,axiom,
! [X12,X15,X13,X16,X45,X14,X46] :
( ( samesideline(X12,X15,X13,X16)
| s_col(X13,X16,X15)
| s_col(X13,X16,X12)
| X15 = X46
| X12 = X45
| X14 = X46
| X14 = X45
| X13 = X16
| ~ s_col(X13,X16,X46)
| ~ s_col(X13,X16,X45)
| ~ s_t(X15,X46,X14)
| ~ s_t(X12,X45,X14) )
& ( ~ s_col(X13,X16,X15)
| ~ samesideline(X12,X15,X13,X16) )
& ( ~ s_col(X13,X16,X12)
| ~ samesideline(X12,X15,X13,X16) )
& ( X13 != X16
| ~ samesideline(X12,X15,X13,X16) )
& ( ss3(X12,X15,X13,X16) != ss2(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( ss3(X12,X15,X13,X16) != ss1(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( X15 != ss2(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( X12 != ss1(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( s_t(X15,ss2(X12,X15,X13,X16),ss3(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_t(X12,ss1(X12,X15,X13,X16),ss3(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_col(X13,X16,ss2(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_col(X13,X16,ss1(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn9_7) ).
fof(c_0_19,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_20,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_19]) ).
fof(c_0_21,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_22,plain,
! [X816,X817,X818] :
( reflect(X816,X817,reflect(X816,X817,X818)) = X818
| X816 = X817 ),
inference(variable_rename,[status(thm)],[aSatz10_5]) ).
fof(c_0_23,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_20])])])]) ).
fof(c_0_24,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_21])]) ).
fof(c_0_25,plain,
! [X12,X15,X13,X16] :
( perp(X12,X15,X16,X13)
| ~ perp(X12,X15,X13,X16) ),
inference(fof_simplification,[status(thm)],[aExtPerp4]) ).
fof(c_0_26,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]) ).
cnf(c_0_27,plain,
( reflect(X1,X2,reflect(X1,X2,X3)) = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
reflect(esk1_0,esk2_0,esk3_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( reflect(X1,X2,X3) != X3
| s_col(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
~ s_col(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_32,plain,
! [X12,X15,X14] :
( s_col(X15,X12,X14)
| ~ s_col(X12,X15,X14) ),
inference(fof_simplification,[status(thm)],[aSatz4_11d]) ).
fof(c_0_33,plain,
! [X12,X15,X13,X16] :
( perp(X15,X12,X13,X16)
| ~ perp(X12,X15,X13,X16) ),
inference(fof_simplification,[status(thm)],[aperp1]) ).
fof(c_0_34,plain,
! [X648,X649,X650,X651] :
( perp(X648,X649,X651,X650)
| ~ perp(X648,X649,X650,X651) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_25])]) ).
cnf(c_0_35,plain,
( perp(X1,X2,X3,reflect(X1,X2,X3))
| X3 = reflect(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
reflect(esk1_0,esk2_0,esk4_0) = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_37,negated_conjecture,
esk4_0 != esk3_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_29]),c_0_31]) ).
fof(c_0_38,plain,
! [X12,X15,X13,X37] :
( X13 = reflect(X12,X15,X37)
| reflect(X12,X15,X13) != X37
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz10_6]) ).
fof(c_0_39,plain,
! [X12,X15,X13,X16] :
( X13 = X16
| reflect(X12,X15,X13) != reflect(X12,X15,X16)
| X12 = X15 ),
inference(fof_simplification,[status(thm)],[aSatz10_7]) ).
fof(c_0_40,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_41,plain,
! [X12,X15,X13,X37] :
( ( X37 = reflect(X12,X15,X13)
| X13 != X37
| ~ s_col(X12,X15,midpoint(X13,X37))
| X12 = X15 )
& ( X37 = reflect(X12,X15,X13)
| ~ perp(X12,X15,X13,X37)
| ~ s_col(X12,X15,midpoint(X13,X37))
| X12 = X15 ) ),
inference(fof_simplification,[status(thm)],[aSatz10_2b]) ).
fof(c_0_42,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_32])]) ).
cnf(c_0_43,plain,
( s_col(X1,X2,midpoint(X3,reflect(X1,X2,X3)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_44,plain,
! [X585,X586,X587,X588] :
( perp(X586,X585,X587,X588)
| ~ perp(X585,X586,X587,X588) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
cnf(c_0_45,plain,
( ~ perp(X1,X2,X3,X4)
| perp(X1,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,negated_conjecture,
perp(esk1_0,esk2_0,esk4_0,esk3_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_29]) ).
fof(c_0_47,plain,
! [X819,X820,X821,X822] :
( X821 = reflect(X819,X820,X822)
| reflect(X819,X820,X821) != X822
| X819 = X820 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
fof(c_0_48,plain,
! [X823,X824,X825,X826] :
( X825 = X826
| reflect(X823,X824,X825) != reflect(X823,X824,X826)
| X823 = X824 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
fof(c_0_49,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_40])]) ).
fof(c_0_50,plain,
! [X808,X809,X810,X811] :
( ( X811 = reflect(X808,X809,X810)
| X810 != X811
| ~ s_col(X808,X809,midpoint(X810,X811))
| X808 = X809 )
& ( X811 = reflect(X808,X809,X810)
| ~ perp(X808,X809,X810,X811)
| ~ s_col(X808,X809,midpoint(X810,X811))
| X808 = X809 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_41])]) ).
cnf(c_0_51,plain,
( ~ s_col(X1,X2,X3)
| s_col(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
s_col(esk1_0,esk2_0,midpoint(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_28]),c_0_29]) ).
cnf(c_0_53,plain,
( ~ perp(X1,X2,X3,X4)
| perp(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
perp(esk1_0,esk2_0,esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
( reflect(X1,X2,X3) != X4
| X3 = reflect(X1,X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( reflect(X1,X2,X3) != reflect(X1,X2,X4)
| X3 = X4
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ s_col(X1,X2,X3)
| reflect(X1,X2,X3) = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( ~ perp(X1,X2,X3,X4)
| ~ s_col(X1,X2,midpoint(X3,X4))
| X4 = reflect(X1,X2,X3)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,negated_conjecture,
s_col(esk2_0,esk1_0,midpoint(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
perp(esk2_0,esk1_0,esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( esk4_0 != X1
| reflect(esk1_0,esk2_0,X1) = esk3_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_29]) ).
cnf(c_0_62,negated_conjecture,
( esk3_0 != X1
| reflect(esk1_0,esk2_0,X1) = esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_29]) ).
fof(c_0_63,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_64,plain,
! [X1,X2] :
( X1 = X2
| ~ s_t(X1,X2,X1) ),
inference(fof_simplification,[status(thm)],[aA6]) ).
fof(c_0_65,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_66,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]) ).
fof(c_0_67,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_68,plain,
( ~ s_col(X3,X4,X2)
| reflect(X3,X4,X1) != X2
| X3 = X4
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,negated_conjecture,
reflect(esk2_0,esk1_0,esk3_0) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),c_0_29]) ).
cnf(c_0_70,negated_conjecture,
( esk3_0 != X1
| esk4_0 != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_37]) ).
fof(c_0_71,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_63])]) ).
fof(c_0_72,plain,
! [X70,X71] :
( X70 = X71
| ~ s_t(X70,X71,X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
fof(c_0_73,plain,
! [X12,X13,X16,X14,X15] :
( ~ samesideline(X12,X15,X13,X16)
| opposite(X15,X13,X16,X14)
| ~ opposite(X12,X13,X16,X14) ),
inference(fof_simplification,[status(thm)],[aSatz9_8]) ).
fof(c_0_74,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_65])]) ).
cnf(c_0_75,negated_conjecture,
~ opposite(esk3_0,esk1_0,esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_76,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_66]) ).
cnf(c_0_77,negated_conjecture,
~ s_col(esk1_0,esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_37]),c_0_29]) ).
fof(c_0_78,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_67])]) ).
fof(c_0_79,plain,
! [X605,X606] : s_m(X605,midpoint(X605,X606),X606),
inference(variable_rename,[status(thm)],[aSatz8_22]) ).
cnf(c_0_80,negated_conjecture,
( ~ s_col(esk2_0,esk1_0,X1)
| esk4_0 != X1 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_29]),c_0_70]) ).
cnf(c_0_81,plain,
( ~ opposite(X1,X2,X3,X4)
| s_col(X2,X3,il(X1,X4,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,plain,
( ~ s_t(X1,X2,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_83,plain,
( ~ opposite(X1,X2,X3,X4)
| s_t(X1,il(X1,X4,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_84,plain,
! [X741,X742,X743,X744,X745] :
( ~ samesideline(X741,X745,X742,X743)
| opposite(X745,X742,X743,X744)
| ~ opposite(X741,X742,X743,X744) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_73])]) ).
cnf(c_0_85,plain,
( ~ samesideline(X1,X2,X3,X4)
| samesideline(X1,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_86,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_75,c_0_76]),c_0_29]),c_0_31]),c_0_77]) ).
fof(c_0_87,plain,
! [X12,X15,X13,X16,X45,X14,X46] :
( ( samesideline(X12,X15,X13,X16)
| s_col(X13,X16,X15)
| s_col(X13,X16,X12)
| X15 = X46
| X12 = X45
| X14 = X46
| X14 = X45
| X13 = X16
| ~ s_col(X13,X16,X46)
| ~ s_col(X13,X16,X45)
| ~ s_t(X15,X46,X14)
| ~ s_t(X12,X45,X14) )
& ( ~ s_col(X13,X16,X15)
| ~ samesideline(X12,X15,X13,X16) )
& ( ~ s_col(X13,X16,X12)
| ~ samesideline(X12,X15,X13,X16) )
& ( X13 != X16
| ~ samesideline(X12,X15,X13,X16) )
& ( ss3(X12,X15,X13,X16) != ss2(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( ss3(X12,X15,X13,X16) != ss1(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( X15 != ss2(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( X12 != ss1(X12,X15,X13,X16)
| ~ samesideline(X12,X15,X13,X16) )
& ( s_t(X15,ss2(X12,X15,X13,X16),ss3(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_t(X12,ss1(X12,X15,X13,X16),ss3(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_col(X13,X16,ss2(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) )
& ( s_col(X13,X16,ss1(X12,X15,X13,X16))
| ~ samesideline(X12,X15,X13,X16) ) ),
inference(fof_simplification,[status(thm)],[d_Defn9_7]) ).
cnf(c_0_88,plain,
( ~ s_m(X1,X2,X3)
| s_t(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,plain,
s_m(X1,midpoint(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,negated_conjecture,
( ~ opposite(X1,esk2_0,esk1_0,X2)
| il(X1,X2,esk2_0,esk1_0) != esk4_0 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_91,plain,
( ~ opposite(X1,X2,X3,X1)
| il(X1,X1,X2,X3) = X1 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
( ~ samesideline(X1,X5,X2,X3)
| ~ opposite(X1,X2,X3,X4)
| opposite(X5,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_93,negated_conjecture,
samesideline(esk3_0,esk4_0,esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_94,plain,
! [X940,X941,X942,X943,X944,X945,X946] :
( ( samesideline(X940,X941,X942,X943)
| s_col(X942,X943,X941)
| s_col(X942,X943,X940)
| X941 = X946
| X940 = X944
| X945 = X946
| X945 = X944
| X942 = X943
| ~ s_col(X942,X943,X946)
| ~ s_col(X942,X943,X944)
| ~ s_t(X941,X946,X945)
| ~ s_t(X940,X944,X945) )
& ( ~ s_col(X942,X943,X941)
| ~ samesideline(X940,X941,X942,X943) )
& ( ~ s_col(X942,X943,X940)
| ~ samesideline(X940,X941,X942,X943) )
& ( X942 != X943
| ~ samesideline(X940,X941,X942,X943) )
& ( ss3(X940,X941,X942,X943) != ss2(X940,X941,X942,X943)
| ~ samesideline(X940,X941,X942,X943) )
& ( ss3(X940,X941,X942,X943) != ss1(X940,X941,X942,X943)
| ~ samesideline(X940,X941,X942,X943) )
& ( X941 != ss2(X940,X941,X942,X943)
| ~ samesideline(X940,X941,X942,X943) )
& ( X940 != ss1(X940,X941,X942,X943)
| ~ samesideline(X940,X941,X942,X943) )
& ( s_t(X941,ss2(X940,X941,X942,X943),ss3(X940,X941,X942,X943))
| ~ samesideline(X940,X941,X942,X943) )
& ( s_t(X940,ss1(X940,X941,X942,X943),ss3(X940,X941,X942,X943))
| ~ samesideline(X940,X941,X942,X943) )
& ( s_col(X942,X943,ss2(X940,X941,X942,X943))
| ~ samesideline(X940,X941,X942,X943) )
& ( s_col(X942,X943,ss1(X940,X941,X942,X943))
| ~ samesideline(X940,X941,X942,X943) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_87])]) ).
cnf(c_0_95,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_71]) ).
cnf(c_0_96,plain,
s_t(X1,midpoint(X1,X2),X2),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,negated_conjecture,
( ~ opposite(X1,esk2_0,esk1_0,X1)
| X1 != esk4_0 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( ~ opposite(esk3_0,esk2_0,esk1_0,X1)
| opposite(esk4_0,esk2_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
( ~ s_col(X3,X4,X2)
| ~ samesideline(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_100,plain,
( ~ s_col(X3,X4,X1)
| ~ samesideline(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_101,plain,
( ~ s_col(X1,X2,midpoint(X3,X4))
| s_col(X1,X2,X3)
| s_col(X1,X2,X4)
| opposite(X3,X1,X2,X4)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
~ opposite(esk3_0,esk2_0,esk1_0,esk4_0),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
~ s_col(esk2_0,esk1_0,esk4_0),
inference(spm,[status(thm)],[c_0_99,c_0_93]) ).
cnf(c_0_104,negated_conjecture,
~ s_col(esk2_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_100,c_0_93]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_59]),c_0_29]),c_0_102]),c_0_103]),c_0_104]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 17:17:41 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 9.43/1.60 % Version: 3.5.1
% 9.43/1.60 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.43/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.43/1.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.43/1.60 % Starting new_bool_3 with 300s (1) cores
% 9.43/1.60 % Starting new_bool_1 with 300s (1) cores
% 9.43/1.60 % Starting sh5l with 300s (1) cores
% 9.43/1.60 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 532106 completed with status 0
% 9.43/1.60 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.43/1.60 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.43/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.43/1.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.43/1.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.43/1.60 % No SInE strategy applied
% 9.43/1.60 % Search class: FGHSM-FSLF33-MFFFFFNN
% 9.43/1.60 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 9.43/1.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.43/1.60 % Starting SubtermCWHack with 136s (1) cores
% 9.43/1.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.43/1.60 % Starting new_bool_3 with 393s (1) cores
% 9.43/1.60 % Starting G-E--_303_C18_F1_URBAN_S0Y with 330s (1) cores
% 9.43/1.60 % Starting Y1006__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 9.43/1.60 % G-E--_303_C18_F1_URBAN_S0Y with pid 532116 completed with status 0
% 9.43/1.60 % Result found by G-E--_303_C18_F1_URBAN_S0Y
% 9.43/1.60 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.43/1.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.43/1.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.43/1.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.43/1.60 % No SInE strategy applied
% 9.43/1.60 % Search class: FGHSM-FSLF33-MFFFFFNN
% 9.43/1.60 % partial match(1): FGHSM-FSLM33-MFFFFFNN
% 9.43/1.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.43/1.60 % Starting SubtermCWHack with 136s (1) cores
% 9.43/1.60 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.43/1.60 % Starting new_bool_3 with 393s (1) cores
% 9.43/1.60 % Starting G-E--_303_C18_F1_URBAN_S0Y with 330s (1) cores
% 9.43/1.60 % Preprocessing time : 0.004 s
% 9.43/1.60
% 9.43/1.60 % Proof found!
% 9.43/1.60 % SZS status Theorem
% 9.43/1.60 % SZS output start CNFRefutation
% See solution above
% 9.43/1.60 % Parsed axioms : 213
% 9.43/1.60 % Removed by relevancy pruning/SinE : 0
% 9.43/1.60 % Initial clauses : 307
% 9.43/1.60 % Removed in clause preprocessing : 1
% 9.43/1.60 % Initial clauses in saturation : 306
% 9.43/1.60 % Processed clauses : 4511
% 9.43/1.60 % ...of these trivial : 109
% 9.43/1.60 % ...subsumed : 2319
% 9.43/1.60 % ...remaining for further processing : 2083
% 9.43/1.60 % Other redundant clauses eliminated : 47
% 9.43/1.60 % Clauses deleted for lack of memory : 0
% 9.43/1.60 % Backward-subsumed : 53
% 9.43/1.60 % Backward-rewritten : 37
% 9.43/1.60 % Generated clauses : 44508
% 9.43/1.60 % ...of the previous two non-redundant : 41232
% 9.43/1.60 % ...aggressively subsumed : 0
% 9.43/1.60 % Contextual simplify-reflections : 107
% 9.43/1.60 % Paramodulations : 44440
% 9.43/1.60 % Factorizations : 2
% 9.43/1.60 % NegExts : 0
% 9.43/1.60 % Equation resolutions : 66
% 9.43/1.60 % Disequality decompositions : 0
% 9.43/1.60 % Total rewrite steps : 4706
% 9.43/1.60 % ...of those cached : 3916
% 9.43/1.60 % Propositional unsat checks : 0
% 9.43/1.60 % Propositional check models : 0
% 9.43/1.60 % Propositional check unsatisfiable : 0
% 9.43/1.60 % Propositional clauses : 0
% 9.43/1.60 % Propositional clauses after purity: 0
% 9.43/1.60 % Propositional unsat core size : 0
% 9.43/1.60 % Propositional preprocessing time : 0.000
% 9.43/1.60 % Propositional encoding time : 0.000
% 9.43/1.60 % Propositional solver time : 0.000
% 9.43/1.60 % Success case prop preproc time : 0.000
% 9.43/1.60 % Success case prop encoding time : 0.000
% 9.43/1.60 % Success case prop solver time : 0.000
% 9.43/1.60 % Current number of processed clauses : 1979
% 9.43/1.60 % Positive orientable unit clauses : 94
% 9.43/1.60 % Positive unorientable unit clauses: 1
% 9.43/1.60 % Negative unit clauses : 64
% 9.43/1.60 % Non-unit-clauses : 1820
% 9.43/1.60 % Current number of unprocessed clauses: 36838
% 9.43/1.60 % ...number of literals in the above : 210603
% 9.43/1.60 % Current number of archived formulas : 0
% 9.43/1.60 % Current number of archived clauses : 91
% 9.43/1.60 % Clause-clause subsumption calls (NU) : 1048198
% 9.43/1.60 % Rec. Clause-clause subsumption calls : 213573
% 9.43/1.60 % Non-unit clause-clause subsumptions : 1537
% 9.43/1.60 % Unit Clause-clause subsumption calls : 9132
% 9.43/1.60 % Rewrite failures with RHS unbound : 0
% 9.43/1.60 % BW rewrite match attempts : 2304
% 9.43/1.60 % BW rewrite match successes : 66
% 9.43/1.60 % Condensation attempts : 0
% 9.43/1.60 % Condensation successes : 0
% 9.43/1.60 % Termbank termtop insertions : 726544
% 9.43/1.60 % Search garbage collected termcells : 2650
% 9.43/1.60
% 9.43/1.60 % -------------------------------------------------
% 9.43/1.60 % User time : 1.181 s
% 9.43/1.60 % System time : 0.044 s
% 9.43/1.60 % Total time : 1.225 s
% 9.43/1.60 % Maximum resident set size: 5304 pages
% 9.43/1.60
% 9.43/1.60 % -------------------------------------------------
% 9.43/1.60 % User time : 5.681 s
% 9.43/1.60 % System time : 0.195 s
% 9.43/1.60 % Total time : 5.876 s
% 9.43/1.60 % Maximum resident set size: 5120 pages
% 9.43/1.60 % E exiting
%------------------------------------------------------------------------------