%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO661+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:26:48 PM UTC 2026
% Result : Satisfiable 0.12s 0.37s
% Output : Saturation 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,V,V2,W] :
( ( equidistant(X,Y,V2,W)
& equidistant(X,Y,Z,V) )
=> equidistant(Z,V,V2,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( equidistant(X,Y,Z,Z)
=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,A,B] :
? [Z] :
( between(X,Y,Z)
=> equidistant(Y,Z,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( ( X != Y
& between(X1,Y1,Z1)
& between(X,Y,Z)
& equidistant(Y,V,Y1,V1)
& equidistant(X,V,X1,V1)
& equidistant(Y,Z,Y1,Z1)
& equidistant(X,Y,X1,Y1) )
=> equidistant(Z,V,Z1,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( between(X,Y,X)
=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,U,Z,Y,V] :
( ( between(Y,V,Z)
& between(X,U,Z) )
=> ? [A] :
( between(V,A,X)
& between(U,A,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
? [A,B,C] :
( ~ between(C,A,B)
& ~ between(B,C,A)
& ~ between(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,W,V,Y,Z] :
( ( W != V
& equidistant(Z,W,Z,V)
& equidistant(Y,W,Y,V)
& equidistant(X,W,X,V) )
=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,U,V,Y,Z] :
( ( X != U
& between(Y,U,Z)
& between(X,U,V) )
=> ? [A,B] :
( between(A,V,B)
& between(X,Z,B)
& between(X,Y,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,V1,X,X1,W] :
( ( between(V,W,X)
& between(U,V,X)
& equidistant(U,X,U,X1)
& equidistant(U,V,U,V1) )
=> ? [A] :
( equidistant(U,W,U,A)
& between(V1,A,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ! [X,Y] :
( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X,Y,A,B] :
? [Z] :
( equidistant(Y,Z,A,B)
| ~ between(X,Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [Y] :
( ! [A,B] :
? [Z] : equidistant(Y,Z,A,B)
| ! [X] :
? [Z] : ~ between(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [Y] :
( ! [A,B] : equidistant(Y,sK1_skl(B,A,Y),A,B)
| ! [X] : ~ between(X,Y,sK0_skl(X,Y)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Z,sK0_skl(X,Y)),skolemize(Z,sK1_skl(B,A,Y))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,sK1_skl(X2,X3,X1),X3,X2)
| ~ between(X0,X1,sK0_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| ! [X,Y] :
( X = Y
| ! [X1,Y1] :
( ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X,U,Z,Y,V] :
( ? [A] :
( between(V,A,X)
& between(U,A,Y) )
| ~ between(Y,V,Z)
| ~ between(X,U,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
! [X,U,Y,V] :
( ? [A] :
( between(V,A,X)
& between(U,A,Y) )
| ! [Z] :
( ~ between(Y,V,Z)
| ~ between(X,U,Z) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [X,U,Y,V] :
( ( between(V,sK2_skl(V,Y,U,X),X)
& between(U,sK2_skl(V,Y,U,X),Y) )
| ! [Z] :
( ~ between(Y,V,Z)
| ~ between(X,U,Z) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(A,sK2_skl(V,Y,U,X))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,sK2_skl(X4,X3,X1,X0),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,sK2_skl(X4,X3,X1,X0),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
( ~ between(sK5_skl,sK3_skl,sK4_skl)
& ~ between(sK4_skl,sK5_skl,sK3_skl)
& ~ between(sK3_skl,sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f8]) ).
fof(f34,plain,
~ between(sK3_skl,sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
~ between(sK4_skl,sK5_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
~ between(sK5_skl,sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [X,W,V,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| W = V
| ~ equidistant(Z,W,Z,V)
| ~ equidistant(Y,W,Y,V)
| ~ equidistant(X,W,X,V) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X,Y,Z] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ! [W,V] :
( W = V
| ~ equidistant(Z,W,Z,V)
| ~ equidistant(Y,W,Y,V)
| ~ equidistant(X,W,X,V) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,X0,X3)
| between(X3,X4,X0)
| between(X0,X3,X4)
| X1 = X2
| ~ equidistant(X4,X1,X4,X2)
| ~ equidistant(X3,X1,X3,X2)
| ~ equidistant(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X,U,V,Y,Z] :
( ? [A,B] :
( between(A,V,B)
& between(X,Z,B)
& between(X,Y,A) )
| X = U
| ~ between(Y,U,Z)
| ~ between(X,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
! [X,V,Y,Z] :
( ? [A,B] :
( between(A,V,B)
& between(X,Z,B)
& between(X,Y,A) )
| ! [U] :
( X = U
| ~ between(Y,U,Z)
| ~ between(X,U,V) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X,V,Y,Z] :
( ( between(sK6_skl(Z,Y,V,X),V,sK7_skl(Z,Y,V,X))
& between(X,Z,sK7_skl(Z,Y,V,X))
& between(X,Y,sK6_skl(Z,Y,V,X)) )
| ! [U] :
( X = U
| ~ between(Y,U,Z)
| ~ between(X,U,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl(Z,Y,V,X)),skolemize(B,sK7_skl(Z,Y,V,X))],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,X3,sK6_skl(X4,X3,X2,X0))
| X0 = X1
| ~ between(X3,X1,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,X4,sK7_skl(X4,X3,X2,X0))
| X0 = X1
| ~ between(X3,X1,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( between(sK6_skl(X4,X3,X2,X0),X2,sK7_skl(X4,X3,X2,X0))
| X0 = X1
| ~ between(X3,X1,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [U,V,V1,X,X1,W] :
( ? [A] :
( equidistant(U,W,U,A)
& between(V1,A,X1) )
| ~ between(V,W,X)
| ~ between(U,V,X)
| ~ equidistant(U,X,U,X1)
| ~ equidistant(U,V,U,V1) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f47,plain,
! [U,V1,X1,W] :
( ? [A] :
( equidistant(U,W,U,A)
& between(V1,A,X1) )
| ! [V,X] :
( ~ between(V,W,X)
| ~ between(U,V,X)
| ~ equidistant(U,X,U,X1)
| ~ equidistant(U,V,U,V1) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [U,V1,X1,W] :
( ( equidistant(U,W,U,sK8_skl(W,X1,V1,U))
& between(V1,sK8_skl(W,X1,V1,U),X1) )
| ! [V,X] :
( ~ between(V,W,X)
| ~ between(U,V,X)
| ~ equidistant(U,X,U,X1)
| ~ equidistant(U,V,U,V1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl(W,X1,V1,U))],[f47]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5] :
( between(X2,sK8_skl(X5,X4,X2,X0),X4)
| ~ between(X1,X5,X3)
| ~ between(X0,X1,X3)
| ~ equidistant(X0,X3,X0,X4)
| ~ equidistant(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X0,X5,X0,sK8_skl(X5,X4,X2,X0))
| ~ between(X1,X5,X3)
| ~ between(X0,X1,X3)
| ~ equidistant(X0,X3,X0,X4)
| ~ equidistant(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X1,X4,X3,X5)
| X2 = X0
| ~ between(X0,X2,X3)
| ~ between(X2,X0,X1)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X2,X4,X0,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f58,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f51,f12]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] :
( equidistant(X0,X4,X0,sK8_skl(X4,X2,X3,X0))
| ~ between(X3,X4,X1)
| ~ between(X0,X3,X1)
| ~ equidistant(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f58,f50]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( between(X3,sK8_skl(X4,X2,X3,X0),X2)
| ~ between(X3,X4,X1)
| ~ between(X0,X3,X1)
| ~ equidistant(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f58,f49]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X1,X4,X2,X5)
| X3 = X0
| ~ between(X3,X0,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X0,X4,X0,X5)
| ~ equidistant(X3,X4,X3,X5)
| ~ equidistant(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f58,f25]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( equidistant(X4,X1,X4,X2)
| X0 = X3
| ~ between(X0,X3,X4)
| ~ between(X0,X3,X4)
| ~ equidistant(X3,X1,X3,X2)
| ~ equidistant(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f63,f58]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( equidistant(X4,X1,X4,X2)
| X0 = X3
| ~ between(X0,X3,X4)
| ~ equidistant(X3,X1,X3,X2)
| ~ equidistant(X0,X1,X0,X2) ),
inference(duplicate_literals_removal,[status(thm)],[f67]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( equidistant(X0,X3,X0,sK8_skl(X3,X2,X1,X0))
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f60,f58]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( between(X1,sK8_skl(X3,X2,X1,X0),X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f61,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO661+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 18:20:47 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.12/0.37 % SZS output start Saturation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.030572 seconds
% 0.12/0.39 % CPU time: 0.094300 seconds
% 0.12/0.39 % Total memory used: 2.036 MB
% 0.12/0.39 % Net memory used: 1.908 MB
%------------------------------------------------------------------------------