%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO270+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 : Fri Sep 25 01:20:38 PM UTC 2026
% Result : Theorem 5.79s 2.18s
% Output : CNFRefutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 112
% Syntax : Number of formulae : 160 ( 14 unt; 0 def)
% Number of atoms : 1437 ( 627 equ)
% Maximal formula atoms : 57 ( 8 avg)
% Number of connectives : 1544 ( 267 ~; 168 |; 972 &)
% ( 8 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-6 aty)
% Number of variables : 886 ( 0 sgn 629 !; 257 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( rpoint(X0)
& vf(vd1047,vd1049) = vf(vd1049,X0)
& vf(vd1049,X0) = vf(X0,vd1047) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(208)') ).
fof(f2,negated_conjecture,
~ ? [X0] :
( rpoint(X0)
& vf(vd1047,vd1049) = vf(vd1049,X0)
& vf(vd1049,X0) = vf(X0,vd1047) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( rpoint(vd1048)
& vd1047 = vd1048
& rpoint(vd1050)
& vd1047 != vd1049
& vd1049 = vd1050 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(conjunct2(207), 4), and(holds(conjunct2(207), 1051, 0), and(pred(conjunct2(207), 1), and(pred(conjunct1(207), 2), pred(conjunct1(207), 1)))))') ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(vskolem1064(X5,X4,X0,X1,X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 0)') ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 1)') ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X2,X0) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 2)') ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X0,X2) = vf(X0,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 3)') ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> ron(vskolem1064(X5,X4,X0,X1,X2,X3),X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 4)') ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> ron(vskolem1064(X5,X4,X0,X1,X2,X3),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 5)') ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> rpoint(vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 6)') ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> rintersect(X4,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 7)') ).
fof(f12,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( ( rcircle(X5)
& rcenter(X2,X5)
& ron(X0,X5) )
=> X5 = vskolem1063(X4,X0,X1,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 8)') ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ( rcircle(vskolem1063(X4,X0,X1,X2,X3))
& rcenter(X2,vskolem1063(X4,X0,X1,X2,X3))
& ron(X0,vskolem1063(X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 9)') ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ! [X4] :
( ( rcircle(X4)
& rcenter(X0,X4)
& ron(X2,X4) )
=> X4 = vskolem1061(X0,X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 10)') ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> ( rcircle(vskolem1061(X0,X1,X2,X3))
& rcenter(X0,vskolem1061(X0,X1,X2,X3))
& ron(X2,vskolem1061(X0,X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 11)') ).
fof(f16,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(X1)
& X0 = X1
& rcenter(X2,X3)
& rpoint(X5)
& X4 = X5
& ron(X4,X3) )
=> ( vf(X2,X0) = vf(X2,X4)
<=> ron(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))') ).
fof(f17,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> vf(X0,X1) = vf(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ron(X0,X2)
& rinside(X1,X2)
& rinside(X0,X3)
& ron(X1,X3) )
=> rintersect(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))') ).
fof(f19,axiom,
! [X0,X1] :
( rcenter(X0,X1)
=> rinside(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
fof(f20,axiom,
! [X0,X1] :
( ( ? [X3] :
( rcircle(X3)
& X0 = X3 )
& ? [X2] :
( rcircle(X2)
& X1 = X2 )
& rintersect(X0,X1) )
=> ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))') ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] :
( ( ? [X36] :
( rpoint(X36)
& X0 = X36 )
& ? [X35] :
( rpoint(X35)
& X1 = X35 )
& ? [X34] :
( rpoint(X34)
& X2 = X34 )
& X0 != X1
& X0 != X2
& X1 != X2
& ? [X33] :
( rpoint(X33)
& X3 = X33 )
& ? [X32] :
( rpoint(X32)
& X4 = X32 )
& ? [X31] :
( rpoint(X31)
& X5 = X31 )
& ? [X30] :
( rpoint(X30)
& X6 = X30 )
& ? [X29] :
( rpoint(X29)
& X7 = X29 )
& ? [X28] :
( rpoint(X28)
& X8 = X28 )
& ? [X27] :
( rpoint(X27)
& X9 = X27 )
& ? [X26] :
( rpoint(X26)
& X10 = X26 )
& ? [X25] :
( rpoint(X25)
& X11 = X25 )
& ? [X24] :
( rpoint(X24)
& X12 = X24 )
& ? [X23] :
( rpoint(X23)
& X13 = X23 )
& ? [X22] :
( rpoint(X22)
& X14 = X22 )
& ? [X21] :
( rpoint(X21)
& X15 = X21 )
& rline(X17)
& ron(X3,X16)
& ron(X4,X16)
& ~ ron(X5,X16)
& ! [X18,X19,X20] :
( ( rpoint(X18)
& rpoint(X19)
& rpoint(X20)
& X18 = X3
& vangle(X20,X19,X18) = vangle(X2,X1,X0)
& vangle(X19,X18,X20) = vangle(X1,X0,X2)
& vangle(X18,X20,X19) = vangle(X0,X2,X1)
& vf(X0,X1) = vf(X18,X19)
& vf(X1,X2) = vf(X19,X20)
& vf(X0,X2) = vf(X18,X20)
& ron(X19,X16)
& ~ rR(X3,X19,X4)
& rS(X20,X5,X16) )
=> ( vf(X6,X7) = vf(X8,X9)
& vangle(X10,X11,X12) = vangle(X13,X14,X15) ) )
& X16 = X17 )
=> ( vf(X6,X7) = vf(X8,X9)
& vangle(X10,X11,X12) = vangle(X13,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))') ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X6] :
( rpoint(X6)
& X0 = X6 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& rcenter(X2,X3)
& rcenter(X2,X4)
& ron(X0,X3)
& ron(X1,X4)
& vf(X2,X0) = vf(X2,X1) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))') ).
fof(f23,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X9] :
( rpoint(X9)
& X0 = X9 )
& ? [X8] :
( rpoint(X8)
& X1 = X8 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& X0 != X1
& X0 != X2
& X0 != X3
& X1 != X2
& X1 != X3
& X2 != X3
& rline(X5)
& X4 = X5
& ~ ron(X3,X4) )
=> ( rR(X2,X0,X1)
<=> vplus(vg(X0,X2,X3),vg(X3,X2,X1)) = vg(X0,X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))') ).
fof(f24,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& X0 != X1
& ron(X0,X3)
& ron(X1,X3) )
=> ( vg(X0,X1,X2) = v0
<=> ron(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))') ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 ) )
=> ? [X6] :
( rreal(X6)
& vg(X0,X1,X2) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))') ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ? [X15] :
( rpoint(X15)
& X0 = X15 )
& ? [X14] :
( rpoint(X14)
& X1 = X14 )
& ? [X13] :
( rpoint(X13)
& X2 = X13 )
& ? [X12] :
( rpoint(X12)
& X3 = X12 )
& ? [X11] :
( rpoint(X11)
& X4 = X11 )
& ? [X10] :
( rline(X10)
& X5 = X10 )
& ? [X9] :
( rline(X9)
& X6 = X9 )
& ? [X8] :
( rline(X8)
& X7 = X8 )
& ron(X0,X5)
& ron(X1,X5)
& ron(X1,X6)
& ron(X2,X6)
& ron(X2,X7)
& ron(X3,X7)
& X1 != X2
& rS(X0,X3,X6)
& rless(vplus(vangle(X0,X1,X2),vangle(X1,X2,X3)),vplus(vperp,vperp)) )
=> ( rintersect(X5,X6)
& ( ( ron(X4,X5)
& ron(X4,X6) )
=> rS(X4,X0,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))') ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X13] :
( rpoint(X13)
& X0 = X13 )
& ? [X12] :
( rpoint(X12)
& X1 = X12 )
& ? [X11] :
( rpoint(X11)
& X2 = X11 )
& ? [X10] :
( rpoint(X10)
& X3 = X10 )
& ? [X9] :
( rpoint(X9)
& X4 = X9 )
& ? [X8] :
( rline(X8)
& X5 = X8 )
& ? [X7] :
( rline(X7)
& X6 = X7 )
& ron(X0,X5)
& ron(X1,X5)
& ron(X3,X5)
& ron(X2,X6)
& ron(X4,X6)
& X1 != X0
& X2 != X0
& X3 != X0
& X4 != X0
& ~ rR(X0,X1,X3)
& ~ rR(X0,X2,X4) )
=> vangle(X1,X0,X2) = vangle(X3,X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))') ).
fof(f28,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X9] :
( rpoint(X9)
& X0 = X9 )
& ? [X8] :
( rpoint(X8)
& X1 = X8 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& rline(X5)
& X4 = X5
& rR(X2,X0,X1)
& ~ ron(X3,X4) )
=> ( vangle(X0,X2,X3) = vangle(X3,X2,X1)
<=> vangle(X0,X2,X3) = vperp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))') ).
fof(f29,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X11] :
( rpoint(X11)
& X0 = X11 )
& ? [X10] :
( rpoint(X10)
& X1 = X10 )
& ? [X9] :
( rpoint(X9)
& X2 = X9 )
& ? [X8] :
( rpoint(X8)
& X3 = X8 )
& ? [X7] :
( rline(X7)
& X4 = X7 )
& ? [X6] :
( rline(X6)
& X5 = X6 )
& ron(X0,X4)
& ron(X0,X5)
& ron(X1,X4)
& ron(X2,X5)
& X0 != X1
& X0 != X2
& ~ ron(X3,X4)
& ~ ron(X3,X5)
& X4 != X5 )
=> ( vangle(X1,X0,X2) = vplus(vangle(X1,X0,X3),vangle(X3,X0,X2))
<=> ( rS(X1,X3,X5)
& rS(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))') ).
fof(f30,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& rpoint(X5)
& X4 = X5
& rline(X7)
& X6 = X7
& X0 != X2
& X0 != X4
& ron(X0,X6)
& ron(X2,X6) )
=> ( ( ron(X4,X6)
& ~ rR(X0,X2,X4) )
<=> vangle(X2,X0,X4) = v0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))') ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& rcenter(X2,X3)
& ron(X1,X3) )
=> ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))') ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 )
& rR(X1,X0,X2) )
=> vplus(vf(X0,X1),vf(X1,X2)) = vf(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))') ).
fof(f33,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X11] :
( rpoint(X11)
& X0 = X11 )
& ? [X10] :
( rpoint(X10)
& X1 = X10 )
& ? [X9] :
( rpoint(X9)
& X2 = X9 )
& ? [X8] :
( rpoint(X8)
& X3 = X8 )
& ? [X7] :
( rpoint(X7)
& X4 = X7 )
& ? [X6] :
( rpoint(X6)
& X5 = X6 )
& vf(X0,X1) = vf(X3,X4)
& vf(X1,X2) = vf(X4,X5)
& vf(X2,X0) = vf(X5,X3)
& vangle(X0,X1,X2) = vangle(X3,X4,X5)
& vangle(X1,X2,X0) = vangle(X4,X5,X3)
& vangle(X2,X0,X1) = vangle(X5,X3,X4) )
=> vg(X0,X1,X2) = vg(X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))') ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 ) )
=> ( vg(X0,X1,X2) = vg(X2,X0,X1)
& vg(X0,X1,X2) = vg(X0,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))') ).
fof(f36,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> vg(X0,X0,X1) = v0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))') ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 )
& X0 != X1
& X0 != X2 )
=> vangle(X0,X1,X2) = vangle(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))') ).
fof(f40,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> ( vf(X0,X1) = v0
<=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
fof(f41,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> ? [X4] :
( rreal(X4)
& vf(X0,X1) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))') ).
fof(f42,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& vplus(X0,X4) = vplus(X2,X4) )
=> X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
fof(f43,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 )
& X0 != X1 )
=> ? [X4] :
( rcircle(X4)
& rcenter(X0,X4)
& ron(X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& rless(X0,X2) )
=> rless(vplus(X0,X4),vplus(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))') ).
fof(f45,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& rless(X0,X2)
& rless(X2,X4) )
=> rless(X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))') ).
fof(f46,axiom,
! [X0,X1] :
( ( rreal(X1)
& X0 = X1 )
=> ~ rless(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))') ).
fof(f47,axiom,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rless(X0,X2) )
=> ( X0 = X2
| ~ rless(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))') ).
fof(f48,axiom,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> ( rless(X2,X0)
| X0 = X2
| rless(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))') ).
fof(f49,axiom,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> vplus(X0,X2) = vplus(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))') ).
fof(f50,axiom,
! [X0,X1] :
( ( rreal(X1)
& X0 = X1 )
=> vplus(X0,v0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))') ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> ? [X4] :
( rreal(X4)
& vplus(X0,X2) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))') ).
fof(f52,axiom,
v0 = vd684,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
fof(f53,axiom,
rreal(vd684),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
fof(f54,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rcircle(X5)
& X2 = X5 )
& ? [X4] :
( rcircle(X4)
& X3 = X4 )
& ron(X0,X2)
& ( rinside(X1,X2)
| ron(X1,X2) )
& rinside(X0,X3)
& ~ ron(X1,X3)
& ~ rinside(X1,X3) )
=> rintersect(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))') ).
fof(f55,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rline(X5)
& X4 = X5
& rinside(X0,X2)
& ron(X0,X4) )
=> rintersect(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))') ).
fof(f56,axiom,
! [X0,X1,X2,X3] :
( ( ? [X8] :
( rpoint(X8)
& X0 = X8 )
& ? [X7] :
( rpoint(X7)
& X1 = X7 )
& ? [X6] :
( rcircle(X6)
& X2 = X6 )
& ? [X5] :
( rcircle(X5)
& X3 = X5 )
& ( rinside(X0,X2)
| ron(X0,X2) )
& ( rinside(X1,X2)
| ron(X1,X2) )
& ~ ? [X4] : rS(X0,X1,X4) )
=> ? [X9] : rintersect(X9,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))') ).
fof(f57,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& rline(X3)
& ~ rS(X0,X1,X2)
& rline(X5)
& ron(X0,X4)
& ron(X1,X4)
& X4 = X5
& X2 = X3 )
=> rintersect(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))') ).
fof(f58,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ? [X11] :
( rcircle(X11)
& X0 = X11 )
& ? [X10] :
( rcircle(X10)
& X1 = X10 )
& X0 != X1
& rintersect(X0,X1)
& ? [X9] :
( rpoint(X9)
& X2 = X9 )
& ? [X8] :
( rpoint(X8)
& X3 = X8 )
& ron(X2,X0)
& ron(X2,X1)
& ron(X3,X0)
& ron(X3,X1)
& X2 != X3
& rcenter(X4,X0)
& rcenter(X5,X1)
& rline(X7)
& X6 = X7
& ron(X4,X6)
& ron(X5,X6) )
=> ~ rS(X2,X3,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))') ).
fof(f59,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rcircle(X4)
& X3 = X4
& ( rinside(X0,X3)
| ron(X0,X3) )
& ~ rinside(X2,X3)
& rR(X2,X0,X1) )
=> ( ~ ron(X1,X3)
& ~ ron(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))') ).
fof(f60,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X9] :
( rpoint(X9)
& X0 = X9 )
& ? [X8] :
( rpoint(X8)
& X1 = X8 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& X3 = X4
& rcircle(X6)
& X5 = X6
& ( rinside(X0,X5)
| ron(X0,X5) )
& ( rinside(X1,X5)
| ron(X1,X5) )
& rR(X2,X0,X1) )
=> rinside(X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))') ).
fof(f61,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X9] :
( rpoint(X9)
& X0 = X9 )
& ? [X8] :
( rpoint(X8)
& X1 = X8 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& X3 = X4
& rcircle(X6)
& X5 = X6
& ron(X0,X3)
& ron(X1,X3)
& ron(X2,X3)
& rinside(X0,X5)
& ron(X1,X5)
& ron(X2,X5)
& X1 != X2 )
=> rR(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))') ).
fof(f62,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ? [X14] :
( rline(X14)
& X0 = X14 )
& ? [X13] :
( rline(X13)
& X1 = X13 )
& ? [X12] :
( rline(X12)
& X2 = X12 )
& ? [X11] :
( rpoint(X11)
& X3 = X11 )
& ? [X10] :
( rpoint(X10)
& X4 = X10 )
& ? [X9] :
( rpoint(X9)
& X5 = X9 )
& ? [X8] :
( rpoint(X8)
& X6 = X8 )
& ron(X3,X0)
& ron(X3,X1)
& ron(X3,X2)
& ron(X4,X0)
& ron(X5,X1)
& ron(X6,X2)
& rS(X5,X6,X0)
& rS(X4,X5,X2)
& rS(X6,X7,X1)
& rS(X5,X7,X2) )
=> rS(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))') ).
fof(f63,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X13] :
( rline(X13)
& X0 = X13 )
& ? [X12] :
( rline(X12)
& X1 = X12 )
& ? [X11] :
( rline(X11)
& X2 = X11 )
& ? [X10] :
( rpoint(X10)
& X3 = X10 )
& ? [X9] :
( rpoint(X9)
& X4 = X9 )
& ? [X8] :
( rpoint(X8)
& X5 = X8 )
& ? [X7] :
( rpoint(X7)
& X6 = X7 )
& ron(X3,X0)
& ron(X3,X1)
& ron(X3,X2)
& ron(X4,X0)
& ron(X5,X1)
& ron(X6,X2)
& rS(X5,X6,X0)
& ~ rS(X4,X6,X1)
& ~ ron(X6,X1)
& X4 != X3 )
=> rS(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))') ).
fof(f64,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X13] :
( rline(X13)
& X0 = X13 )
& ? [X12] :
( rline(X12)
& X1 = X12 )
& ? [X11] :
( rline(X11)
& X2 = X11 )
& ? [X10] :
( rpoint(X10)
& X3 = X10 )
& ? [X9] :
( rpoint(X9)
& X4 = X9 )
& ? [X8] :
( rpoint(X8)
& X5 = X8 )
& ? [X7] :
( rpoint(X7)
& X6 = X7 )
& ron(X3,X0)
& ron(X3,X1)
& ron(X3,X2)
& ron(X4,X0)
& ron(X5,X2)
& ron(X6,X2)
& rS(X5,X6,X0)
& rS(X4,X5,X2) )
=> ~ rS(X4,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))') ).
fof(f65,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X9] :
( rpoint(X9)
& X0 = X9 )
& ? [X8] :
( rpoint(X8)
& X1 = X8 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& X0 != X1
& X0 != X2
& X1 != X2
& ? [X6] :
( rline(X6)
& X3 = X6 )
& ? [X5] :
( rline(X5)
& X4 = X5 )
& X3 != X4
& ron(X0,X4)
& ron(X2,X4)
& ~ rS(X0,X2,X3)
& ron(X1,X4)
& ron(X1,X3) )
=> rR(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))') ).
fof(f66,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& rR(X1,X0,X2)
& ron(X1,X3) )
=> ~ rS(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
fof(f67,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& rR(X1,X0,X2)
& ron(X0,X3)
& ~ ron(X1,X3) )
=> rS(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))') ).
fof(f68,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& rR(X1,X0,X2)
& rS(X0,X2,X3) )
=> rS(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))') ).
fof(f69,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& ~ ron(X0,X3)
& ~ ron(X1,X3)
& ~ ron(X2,X3)
& ~ rS(X0,X1,X3) )
=> ( rS(X1,X2,X3)
| rS(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))') ).
fof(f70,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& X3 = X4
& rS(X0,X1,X3)
& rS(X0,X2,X3) )
=> rS(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))') ).
fof(f71,axiom,
! [X0,X1,X2,X3] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& rline(X3)
& X2 = X3
& rS(X0,X1,X2) )
=> ~ ron(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).
fof(f72,axiom,
! [X0,X1,X2,X3] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& rline(X3)
& X2 = X3
& rS(X0,X1,X2) )
=> rS(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))') ).
fof(f73,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& ~ ron(X0,X2) )
=> rS(X0,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))') ).
fof(f74,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& rR(X1,X0,X2)
& rR(X1,X0,X3) )
=> ~ rR(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))') ).
fof(f75,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& X0 != X1
& X0 != X2
& X1 != X2
& rline(X4)
& ron(X0,X3)
& ron(X1,X3)
& ron(X2,X3)
& X3 = X4 )
=> ( rR(X2,X0,X1)
| rR(X0,X1,X2)
| rR(X1,X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))') ).
fof(f76,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& rR(X1,X0,X2)
& rR(X2,X1,X3) )
=> rR(X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))') ).
fof(f77,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& rR(X1,X0,X2)
& rR(X3,X0,X1) )
=> rR(X3,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))') ).
fof(f78,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& rR(X1,X0,X2)
& ron(X0,X3)
& ron(X2,X3)
& X3 = X4 )
=> ron(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))') ).
fof(f79,axiom,
! [X0,X1,X2,X3,X4] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rline(X4)
& rR(X1,X0,X2)
& ron(X0,X3)
& ron(X1,X3)
& X3 = X4 )
=> ron(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))') ).
fof(f80,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 )
& rR(X1,X0,X2) )
=> ( rR(X1,X2,X0)
& X0 != X1
& X0 != X2
& ~ rR(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
fof(f81,axiom,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rinside(X0,X2) )
=> ~ ron(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))') ).
fof(f82,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rcenter(X2,X0)
& rcenter(X3,X0) )
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))') ).
fof(f83,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& X0 != X1
& ? [X5] :
( rline(X5)
& X2 = X5 )
& ? [X4] :
( rline(X4)
& X3 = X4 )
& ron(X0,X2)
& ron(X0,X3)
& ron(X1,X2)
& ron(X1,X3) )
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
fof(f84,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X8] :
( rcircle(X8)
& X0 = X8 )
& ? [X7] :
( rcircle(X7)
& X1 = X7 )
& rline(X3)
& X2 = X3
& rintersect(X0,X1)
& rcenter(X4,X0)
& rcenter(X5,X1)
& ron(X4,X2)
& ron(X5,X2)
& ~ ron(X6,X2) )
=> ? [X9] :
( rpoint(X9)
& ron(X9,X0)
& ron(X9,X1)
& ~ rS(X9,X6,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))') ).
fof(f85,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ? [X8] :
( rcircle(X8)
& X0 = X8 )
& ? [X7] :
( rcircle(X7)
& X1 = X7 )
& rline(X3)
& X2 = X3
& rintersect(X0,X1)
& rcenter(X4,X0)
& rcenter(X5,X1)
& ron(X4,X2)
& ron(X5,X2)
& ~ ron(X6,X2) )
=> ? [X9] :
( rpoint(X9)
& ron(X9,X0)
& ron(X9,X1)
& rS(X9,X6,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))') ).
fof(f86,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rintersect(X0,X2) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))') ).
fof(f87,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rpoint(X5)
& X4 = X5
& rinside(X4,X0)
& ron(X4,X2)
& rpoint(X7)
& X6 = X7
& ron(X6,X2)
& X6 != X4 )
=> ? [X8] :
( rpoint(X8)
& ron(X8,X0)
& ron(X8,X2)
& rR(X4,X8,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))') ).
fof(f88,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rpoint(X5)
& X4 = X5
& rinside(X4,X0)
& ron(X4,X2)
& rpoint(X7)
& X6 = X7
& ~ rinside(X6,X0)
& ~ ron(X6,X0)
& ron(X6,X2) )
=> ? [X8] :
( rpoint(X8)
& ron(X8,X2)
& ron(X8,X0)
& rR(X8,X4,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))') ).
fof(f89,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X2,X0) )
=> ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))') ).
fof(f90,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))') ).
fof(f91,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X0,X2) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))') ).
fof(f92,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 )
& X0 != X1 )
=> ? [X4] :
( rline(X4)
& ron(X0,X4)
& ron(X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
fof(f93,axiom,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ~ rinside(X2,X0)
& ~ ron(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))') ).
fof(f94,axiom,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& rinside(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))') ).
fof(f95,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& ron(X2,X0)
& ron(X3,X0) )
=> ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X6 != X2
& X6 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))') ).
fof(f96,axiom,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& ron(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X4 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))') ).
fof(f97,axiom,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ron(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))') ).
fof(f98,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& X2 = X3 )
=> ? [X4] :
( rpoint(X4)
& ~ rS(X4,X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))') ).
fof(f99,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& rpoint(X5)
& rS(X4,X2,X0)
& rpoint(X7)
& rS(X6,X2,X0)
& X6 = X7
& X4 = X5
& X2 = X3 )
=> ? [X8] :
( rpoint(X8)
& rS(X8,X2,X0)
& X8 != X2
& X8 != X4
& X8 != X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))') ).
fof(f100,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& rpoint(X5)
& rS(X4,X2,X0)
& X4 = X5
& X2 = X3 )
=> ? [X6] :
( rpoint(X6)
& rS(X6,X2,X0)
& X6 != X2
& X6 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))') ).
fof(f101,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& X2 = X3 )
=> ? [X4] :
( rpoint(X4)
& rS(X4,X2,X0)
& X4 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))') ).
fof(f102,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& ron(X2,X0)
& ron(X3,X0)
& rpoint(X5)
& rR(X3,X2,X4)
& X4 = X5 )
=> ? [X8] :
( rpoint(X8)
& rR(X3,X2,X8)
& X8 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))') ).
fof(f103,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& ron(X2,X0)
& ron(X3,X0)
& X2 != X3 )
=> ? [X6] :
( rpoint(X6)
& rR(X3,X2,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))') ).
fof(f104,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& ? [X9] :
( rpoint(X9)
& X2 = X9 )
& ? [X8] :
( rpoint(X8)
& X3 = X8 )
& ? [X7] :
( rpoint(X7)
& X4 = X7 )
& ? [X6] :
( rpoint(X6)
& X5 = X6 )
& ron(X2,X0)
& ron(X3,X0)
& ron(X4,X0)
& rR(X4,X2,X3)
& rR(X5,X2,X3) )
=> ? [X10] :
( rpoint(X10)
& rR(X10,X2,X3)
& X10 != X4
& X10 != X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))') ).
fof(f105,axiom,
! [X0,X1,X2,X3,X4] :
( ( rline(X1)
& X0 = X1
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& ? [X5] :
( rpoint(X5)
& X4 = X5 )
& ron(X2,X0)
& ron(X3,X0)
& rR(X4,X2,X3) )
=> ? [X8] :
( rpoint(X8)
& rR(X8,X2,X3)
& X8 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))') ).
fof(f106,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 )
& ron(X2,X0)
& ron(X3,X0)
& X2 != X3 )
=> ? [X6] :
( rpoint(X6)
& rR(X6,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))') ).
fof(f107,axiom,
! [X0,X1,X2,X3,X4] :
( ( rline(X1)
& X0 = X1
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& ? [X5] :
( rpoint(X5)
& X4 = X5 )
& ron(X2,X0)
& ron(X3,X0)
& ron(X4,X0) )
=> ? [X8] :
( rpoint(X8)
& ron(X8,X0)
& X8 != X2
& X8 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))') ).
fof(f108,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& rpoint(X5)
& X4 = X5
& ron(X2,X0)
& ron(X4,X0) )
=> ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X6 != X2
& X6 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))') ).
fof(f109,axiom,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& ron(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X4 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))') ).
fof(f110,axiom,
! [X0,X1] :
( ( rline(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ron(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))') ).
fof(f111,axiom,
! [X0,X1,X2,X3] :
( ( ? [X7] :
( rpoint(X7)
& X0 = X7 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& ? [X4] :
( rpoint(X4)
& X3 = X4 ) )
=> ? [X8] :
( rpoint(X8)
& X8 != X0
& X8 != X1
& X8 != X2
& X8 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))') ).
fof(f112,axiom,
! [X0,X1,X2] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X3] :
( rpoint(X3)
& X2 = X3 ) )
=> ? [X6] :
( rpoint(X6)
& X6 != X0
& X6 != X1
& X6 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))') ).
fof(f113,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> ? [X4] :
( rpoint(X4)
& X4 != X0
& X4 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))') ).
fof(f114,axiom,
! [X0,X1] :
( ( rpoint(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& X2 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))') ).
fof(f115,axiom,
rpoint(vd14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
fof(f117,axiom,
! [X0,X1] :
( rcenter(X0,X1)
=> ? [X2,X3] :
( rpoint(X2)
& X0 = X2
& rcircle(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))') ).
fof(f122,plain,
! [X0] :
( ~ rpoint(X0)
| vf(vd1049,X0) != vf(vd1047,vd1049)
| vf(vd1049,X0) != vf(X0,vd1047) ),
inference(ennf_transformation,[],[f2]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(vskolem1064(X5,X4,X0,X1,X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(vskolem1064(X5,X4,X0,X1,X2,X3),X0) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
inference(flattening,[],[f125]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| rpoint(vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| ! [X4] :
( vskolem1061(X0,X1,X2,X3) != X4
| ! [X5] :
( vskolem1063(X4,X0,X1,X2,X3) != X5
| rpoint(vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
inference(flattening,[],[f135]) ).
fof(f407,plain,
! [X0] :
( ~ rpoint(X0)
| vf(vd1049,X0) != vf(vd1047,vd1049)
| vf(vd1049,X0) != vf(X0,vd1047) ),
inference(cnf_transformation,[],[f122]) ).
fof(f408,plain,
rpoint(vd1048),
inference(cnf_transformation,[],[f3]) ).
fof(f409,plain,
vd1047 = vd1048,
inference(cnf_transformation,[],[f3]) ).
fof(f410,plain,
rpoint(vd1050),
inference(cnf_transformation,[],[f3]) ).
fof(f411,plain,
vd1049 != vd1047,
inference(cnf_transformation,[],[f3]) ).
fof(f412,plain,
vd1049 = vd1050,
inference(cnf_transformation,[],[f3]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(vskolem1064(X5,X4,X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| vskolem1063(X4,X0,X1,X2,X3) != X5
| vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(X0,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| vskolem1063(X4,X0,X1,X2,X3) != X5
| rpoint(vskolem1064(X5,X4,X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f654,plain,
! [X0] :
( ~ rpoint(X0)
| vf(vd1050,X0) != vf(vd1048,vd1050)
| vf(vd1050,X0) != vf(X0,vd1048) ),
inference(definition_unfolding,[],[f407,f412,f409,f412,f409,f412]) ).
fof(f655,plain,
vd1050 != vd1048,
inference(definition_unfolding,[],[f411,f412,f409]) ).
fof(f665,plain,
! [X2,X3,X0,X1,X4] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| vf(X2,vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3)) = vf(vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3),X0) ),
inference(equality_resolution,[],[f413]) ).
fof(f666,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vf(X2,vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3)) = vf(vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),X0) ),
inference(equality_resolution,[],[f665]) ).
fof(f667,plain,
! [X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X3
| vf(X3,vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3)) = vf(vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),X0) ),
inference(equality_resolution,[],[f666]) ).
fof(f668,plain,
! [X3,X1] :
( ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3
| vf(X3,vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3)) = vf(vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),X1) ),
inference(equality_resolution,[],[f667]) ).
fof(f669,plain,
! [X2,X3,X0,X1,X4] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| vf(X0,X2) = vf(X2,vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3)) ),
inference(equality_resolution,[],[f414]) ).
fof(f670,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vf(X0,X2) = vf(X2,vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3)) ),
inference(equality_resolution,[],[f669]) ).
fof(f671,plain,
! [X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X3
| vf(X3,vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3)) = vf(X0,X3) ),
inference(equality_resolution,[],[f670]) ).
fof(f672,plain,
! [X3,X1] :
( ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3
| vf(X3,vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3)) = vf(X1,X3) ),
inference(equality_resolution,[],[f671]) ).
fof(f689,plain,
! [X2,X3,X0,X1,X4] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| vskolem1061(X0,X1,X2,X3) != X4
| rpoint(vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3)) ),
inference(equality_resolution,[],[f419]) ).
fof(f690,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3
| rpoint(vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3)) ),
inference(equality_resolution,[],[f689]) ).
fof(f691,plain,
! [X3,X0,X1] :
( ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X3
| rpoint(vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3)) ),
inference(equality_resolution,[],[f690]) ).
fof(f692,plain,
! [X3,X1] :
( ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3
| rpoint(vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3)) ),
inference(equality_resolution,[],[f691]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ rpoint(X0)
| ( vf(vd1050,X0) != vf(vd1048,vd1050) )
| ( vf(X0,vd1048) != vf(vd1050,X0) ) ),
inference(cnf_transformation,[],[f654]) ).
tcf(c_50,plain,
vd1050 != vd1048,
inference(cnf_transformation,[],[f655]) ).
tcf(c_51,plain,
rpoint(vd1050),
inference(cnf_transformation,[],[f410]) ).
tcf(c_52,plain,
rpoint(vd1048),
inference(cnf_transformation,[],[f408]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( vf(vskolem1064(vskolem1063(vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0),vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0),X1) = vf(X0,vskolem1064(vskolem1063(vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0),vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0)) )
| ~ rpoint(X1)
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f668]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( vf(X0,vskolem1064(vskolem1063(vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0),vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0)) = vf(X1,X0) )
| ~ rpoint(X1)
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f672]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0),vskolem1061(X1,X1,X0,X0),X1,X1,X0,X0))
| ( X0 = X1 )
| ~ rpoint(X1)
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f692]) ).
tcf(c_5041,plain,
! [X0_iProver_rpoint_1: iProver_rpoint_1,X1_iProver_rpoint_1: iProver_rpoint_1] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1))
| ( X0_iProver_rpoint_1 = X1_iProver_rpoint_1 )
| ~ rpoint(X1_iProver_rpoint_1)
| ~ rpoint(X0_iProver_rpoint_1) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_5046,plain,
! [X0_iProver_rpoint_1: iProver_rpoint_1,X1_iProver_rpoint_1: iProver_rpoint_1] :
( ( X0_iProver_rpoint_1 = X1_iProver_rpoint_1 )
| ( vf(X0_iProver_rpoint_1,vskolem1064(vskolem1063(vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1)) = vf(X1_iProver_rpoint_1,X0_iProver_rpoint_1) )
| ~ rpoint(X1_iProver_rpoint_1)
| ~ rpoint(X0_iProver_rpoint_1) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_5047,plain,
! [X0_iProver_rpoint_1: iProver_rpoint_1,X1_iProver_rpoint_1: iProver_rpoint_1] :
( ( X0_iProver_rpoint_1 = X1_iProver_rpoint_1 )
| ( vf(vskolem1064(vskolem1063(vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1) = vf(X0_iProver_rpoint_1,vskolem1064(vskolem1063(vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),vskolem1061(X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1),X1_iProver_rpoint_1,X1_iProver_rpoint_1,X0_iProver_rpoint_1,X0_iProver_rpoint_1)) )
| ~ rpoint(X1_iProver_rpoint_1)
| ~ rpoint(X0_iProver_rpoint_1) ),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_5050,plain,
vd1050 != vd1048,
inference(subtyping,[status(esa)],[c_50]) ).
tcf(c_5051,negated_conjecture,
! [X0_iProver_rpoint_1: iProver_rpoint_1] :
( ~ rpoint(X0_iProver_rpoint_1)
| ( vf(vd1050,X0_iProver_rpoint_1) != vf(vd1048,vd1050) )
| ( vf(X0_iProver_rpoint_1,vd1048) != vf(vd1050,X0_iProver_rpoint_1) ) ),
inference(subtyping,[status(esa)],[c_49]) ).
tcf(c_9959,plain,
( rpoint(vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050))
| ( vd1050 = vd1048 )
| ~ rpoint(vd1048)
| ~ rpoint(vd1050) ),
inference(instantiation,[status(thm)],[c_5041]) ).
tcf(c_10232,plain,
( ( vd1050 = vd1048 )
| ( vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050)) = vf(vd1048,vd1050) )
| ~ rpoint(vd1048)
| ~ rpoint(vd1050) ),
inference(instantiation,[status(thm)],[c_5046]) ).
tcf(c_10466,plain,
( ( vd1050 = vd1048 )
| ( vf(vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vd1048) = vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050)) )
| ~ rpoint(vd1048)
| ~ rpoint(vd1050) ),
inference(instantiation,[status(thm)],[c_5047]) ).
tcf(c_12729,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050))
| ( vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050)) != vf(vd1048,vd1050) )
| ( vf(vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vd1048) != vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050),vskolem1061(vd1048,vd1048,vd1050,vd1050),vd1048,vd1048,vd1050,vd1050)) ) ),
inference(instantiation,[status(thm)],[c_5051]) ).
tcf(c_12730,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12729,c_10466,c_10232,c_9959,c_5050,c_51,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO270+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:46:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 5.79/2.18 % SZS status Started for theBenchmark.p
% 5.79/2.18 % SZS status Theorem for theBenchmark.p
% 5.79/2.18
% 5.79/2.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.79/2.18
% 5.79/2.18 % ------ iProver source info
% 5.79/2.18
% 5.79/2.18 % git: date: 2026-07-19 20:42:38 +0200
% 5.79/2.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.79/2.18 % git: non_committed_changes: false
% 5.79/2.18
% 5.79/2.18 % ------ Parsing...
% 5.79/2.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.79/2.18
% 5.79/2.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.79/2.18
% 5.79/2.18 % ------ Preprocessing... gs_s sp: 14 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.79/2.18
% 5.79/2.18 % ------ Preprocessing... sf_s rm: 8 0s sf_e
% 5.79/2.18 % ------ Proving...
% 5.79/2.18 % ------ Problem Properties
% 5.79/2.18
% 5.79/2.18 %
% 5.79/2.18 % clauses 250
% 5.79/2.18 % conjectures 1
% 5.79/2.18 % EPR 56
% 5.79/2.18 % Horn 161
% 5.79/2.18 % unary 5
% 5.79/2.18 % binary 42
% 5.79/2.18 % lits 1507
% 5.79/2.18 % lits eq 183
% 5.79/2.18 % fd_pure 0
% 5.79/2.18 % fd_pseudo 0
% 5.79/2.18 % fd_cond 0
% 5.79/2.18 % fd_pseudo_cond 58
% 5.79/2.18 % AC symbols 0
% 5.79/2.18
% 5.79/2.18 % ------ Input Options Time Limit: Unbounded
% 5.79/2.18
% 5.79/2.18
% 5.79/2.18 % ------
% 5.79/2.18 % Current options:
% 5.79/2.18 % ------
% 5.79/2.18
% 5.79/2.18
% 5.79/2.18 %
% 5.79/2.18
% 5.79/2.18 % ------ Proving...
% 5.79/2.18 %
% 5.79/2.18
% 5.79/2.18 % SZS status Theorem for theBenchmark.p
% 5.79/2.18
% 5.79/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.79/2.19
%------------------------------------------------------------------------------