%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 01:19:46 PM UTC 2026
% Result : Unsatisfiable 70.29s 12.06s
% Output : CNFRefutation 70.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 25
% Syntax : Number of formulae : 113 ( 29 unt; 0 def)
% Number of atoms : 292 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 348 ( 169 ~; 179 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 185 ( 0 sgn 185 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f22,axiom,
! [X2,X0,X1] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f27,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
fof(f31,axiom,
! [X2,X3,X0,X1] :
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
fof(f58,axiom,
! [X2,X0,X1] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f59,axiom,
! [X0,X1] : between(X0,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
fof(f60,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f61,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
fof(f65,axiom,
! [X2,X3,X0,X1] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
fof(f67,axiom,
! [X2,X3,X0,X1] :
( X1 = X2
| between(X0,X1,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
fof(f68,axiom,
! [X2,X3,X0,X1] :
( between(X0,X3,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
fof(f89,axiom,
! [X2,X3,X0,X1,X4,X5] :
( between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b11) ).
fof(f93,axiom,
! [X2,X3,X0,X1] :
( between(X0,X3,X1)
| between(X0,X1,X3)
| ~ between(X0,X3,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9) ).
fof(f95,axiom,
! [X2,X3,X0,X1,X4] :
( between(X0,X3,X2)
| ~ between(X0,X4,X2)
| ~ between(X1,X3,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8) ).
fof(f103,axiom,
! [X2,X0,X1] :
( colinear(X2,X0,X1)
| ~ colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_4) ).
fof(f118,axiom,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
fof(f119,axiom,
equidistant(v,w,x,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_x_to_u) ).
fof(f120,axiom,
equidistant(u,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_v_to_x) ).
fof(f121,axiom,
between(u,y,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_between_u_and_w) ).
fof(f122,axiom,
between(v,y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_between_v_and_x) ).
fof(f123,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f124,axiom,
x != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_u) ).
fof(f125,plain,
u != x,
inference(reorient_equations,[],[f124]) ).
fof(f126,negated_conjecture,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_uvw_not_colinear) ).
tcf(c_163,plain,
equidistant(u,v,w,x),
inference(cnf_transformation,[],[f118]) ).
tcf(c_164,plain,
equidistant(v,w,x,u),
inference(cnf_transformation,[],[f119]) ).
tcf(c_165,plain,
equidistant(u,w,v,x),
inference(cnf_transformation,[],[f120]) ).
tcf(c_166,plain,
between(u,y,w),
inference(cnf_transformation,[],[f121]) ).
tcf(c_167,plain,
between(v,y,x),
inference(cnf_transformation,[],[f122]) ).
tcf(c_168,plain,
u != v,
inference(cnf_transformation,[],[f123]) ).
tcf(c_169,plain,
u != x,
inference(cnf_transformation,[],[f125]) ).
tcf(c_170,negated_conjecture,
colinear(u,v,w),
inference(cnf_transformation,[],[f126]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( between(X5,X2,X3)
| ~ between(X4,X0,X1)
| ~ equidistant(X4,X1,X5,X3)
| ~ equidistant(X4,X0,X5,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X3,X1,X4)
| ~ between(X3,X2,X4)
| ~ between(X3,X0,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X0,X3,X1)
| between(X0,X1,X3)
| ~ between(X0,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X1,X2)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X0,X2)
| ( X0 = X1 )
| ~ between(X3,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] : between(X0,X0,X1),
inference(cnf_transformation,[],[f59]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( colinear(X2,X0,X1)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_1033,plain,
! [X0: $i] :
( ( u = x )
| ~ between(X0,x,u)
| ~ between(X0,u,x) ),
inference(instantiation,[status(thm)],[c_208]) ).
tcf(c_1193,plain,
( ( u = x )
| ~ between(x,x,u)
| ~ between(x,u,x) ),
inference(instantiation,[status(thm)],[c_1033]) ).
tcf(c_1194,plain,
between(x,x,u),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_1342,plain,
! [X0: $i] :
( ( u = x )
| ~ between(x,u,X0)
| ~ between(u,x,X0) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_2063,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X0,u,v)
| ~ equidistant(u,v,X0,X1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_2072,plain,
equidistant(v,u,u,v),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_2119,plain,
! [X0: $i,X1: $i] :
( equidistant(u,x,X0,X1)
| ~ equidistant(X0,X1,x,u) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_2298,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X0,X2,v)
| ~ equidistant(X0,X1,v,X2) ),
inference(instantiation,[status(thm)],[c_185]) ).
tcf(c_2647,plain,
! [X0: $i] :
( between(x,u,x)
| ( u = X0 )
| ~ between(x,u,X0)
| ~ between(u,X0,x) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_2817,plain,
( ( u = x )
| ~ between(x,u,v)
| ~ between(u,x,v) ),
inference(instantiation,[status(thm)],[c_1342]) ).
tcf(c_2941,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X0,v,X1,X2)
| ~ equidistant(v,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_187]) ).
tcf(c_2945,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,v,X0,X1)
| ~ equidistant(X0,X1,v,X2) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_2984,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,x,X0,X1)
| ~ equidistant(X0,X1,X2,x) ),
inference(instantiation,[status(thm)],[c_188]) ).
tcf(c_6531,plain,
( equidistant(x,w,u,v)
| ~ equidistant(u,v,w,x) ),
inference(instantiation,[status(thm)],[c_2063]) ).
tcf(c_6940,plain,
( equidistant(u,x,v,w)
| ~ equidistant(v,w,x,u) ),
inference(instantiation,[status(thm)],[c_2119]) ).
tcf(c_7131,plain,
( equidistant(w,u,x,v)
| ~ equidistant(u,w,v,x) ),
inference(instantiation,[status(thm)],[c_2298]) ).
tcf(c_7365,plain,
( equidistant(w,v,x,u)
| ~ equidistant(v,w,x,u) ),
inference(instantiation,[status(thm)],[c_2941]) ).
tcf(c_7484,plain,
( equidistant(x,v,u,w)
| ~ equidistant(u,w,v,x) ),
inference(instantiation,[status(thm)],[c_2945]) ).
tcf(c_11998,plain,
( between(x,u,x)
| ( u = v )
| ~ between(x,u,v)
| ~ between(u,v,x) ),
inference(instantiation,[status(thm)],[c_2647]) ).
tcf(c_15307,plain,
( equidistant(v,x,u,w)
| ~ equidistant(u,w,v,x) ),
inference(instantiation,[status(thm)],[c_2984]) ).
tcf(c_15883,plain,
! [X0: $i] :
( between(X0,v,u)
| ~ between(u,v,X0) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_15915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X2,x,u)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X3,x,u)
| ~ equidistant(X0,X3,X2,u)
| ~ equidistant(X0,X1,X2,x) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_15926,plain,
! [X0: $i,X1: $i] :
( between(u,v,X0)
| between(u,X0,v)
| ~ between(u,v,X1)
| ~ between(u,X0,X1) ),
inference(instantiation,[status(thm)],[c_197]) ).
tcf(c_15934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(u,v,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X3,X0,u,v)
| ~ equidistant(X3,X1,u,X2)
| ~ equidistant(X0,X1,v,X2) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_15942,plain,
! [X0: $i] :
( between(u,x,X0)
| ~ between(X0,x,u) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_16806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X2,v,X3)
| ~ between(X0,X4,X1)
| ~ equidistant(X4,X1,v,X3)
| ~ equidistant(X0,X4,X2,v)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_16935,plain,
! [X0: $i] : between(v,v,X0),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_17213,plain,
! [X0: $i] :
( between(u,x,v)
| between(u,v,x)
| ~ between(u,x,X0)
| ~ between(u,v,X0) ),
inference(instantiation,[status(thm)],[c_15926]) ).
tcf(c_17355,plain,
! [X0: $i] : equidistant(X0,v,v,X0),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_17599,plain,
! [X0: $i,X1: $i] :
( between(X1,x,u)
| ~ between(X0,v,w)
| ~ equidistant(v,w,x,u)
| ~ equidistant(X0,w,X1,u)
| ~ equidistant(X0,v,X1,x) ),
inference(instantiation,[status(thm)],[c_15915]) ).
tcf(c_18877,plain,
! [X0: $i,X1: $i] :
( between(u,v,X1)
| ~ between(v,u,X0)
| ~ equidistant(v,u,u,v)
| ~ equidistant(v,X0,u,X1)
| ~ equidistant(u,X0,v,X1) ),
inference(instantiation,[status(thm)],[c_15934]) ).
tcf(c_26643,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,v,X1)
| ~ between(X0,X1,v)
| ~ equidistant(X1,v,v,X1)
| ~ equidistant(X0,v,X2,X1)
| ~ equidistant(X0,X1,X2,v) ),
inference(instantiation,[status(thm)],[c_16806]) ).
tcf(c_29586,plain,
! [X0: $i,X1: $i] :
( between(v,u,x)
| ~ between(v,X1,x)
| ~ between(v,X0,x)
| ~ between(X0,u,X1) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_43497,plain,
between(v,v,x),
inference(instantiation,[status(thm)],[c_16935]) ).
tcf(c_49164,plain,
! [X0: $i] :
( between(x,X0,v)
| ~ between(v,X0,x) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_49172,plain,
! [X0: $i,X1: $i] :
( between(x,X1,v)
| ~ between(x,X0,v)
| ~ between(X0,X1,v) ),
inference(instantiation,[status(thm)],[c_202]) ).
tcf(c_49421,plain,
equidistant(u,w,w,u),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_50620,plain,
equidistant(w,v,v,w),
inference(instantiation,[status(thm)],[c_17355]) ).
tcf(c_55113,plain,
( between(u,v,w)
| ~ between(v,u,x)
| ~ equidistant(v,x,u,w)
| ~ equidistant(v,u,u,v)
| ~ equidistant(u,x,v,w) ),
inference(instantiation,[status(thm)],[c_18877]) ).
tcf(c_56224,plain,
( between(w,u,v)
| between(v,w,u)
| between(u,v,w)
| ~ colinear(w,u,v) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_58567,plain,
! [X0: $i] :
( between(v,u,x)
| ~ between(v,v,x)
| ~ between(v,X0,x)
| ~ between(X0,u,v) ),
inference(instantiation,[status(thm)],[c_29586]) ).
tcf(c_62407,plain,
( between(x,y,v)
| ~ between(v,y,x) ),
inference(instantiation,[status(thm)],[c_49164]) ).
tcf(c_65399,plain,
( between(u,w,v)
| ~ between(v,w,u) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_80598,plain,
! [X0: $i] :
( between(x,X0,v)
| ~ between(x,y,v)
| ~ between(y,X0,v) ),
inference(instantiation,[status(thm)],[c_49172]) ).
tcf(c_88572,plain,
! [X0: $i] :
( between(y,u,v)
| ~ between(X0,y,u)
| ~ between(X0,u,v) ),
inference(instantiation,[status(thm)],[c_205]) ).
tcf(c_118362,plain,
! [X0: $i] :
( between(X0,y,u)
| ~ between(u,y,X0) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_123585,plain,
! [X0: $i,X1: $i] :
( between(y,X1,v)
| ~ between(X0,y,X1)
| ~ between(X0,X1,v) ),
inference(instantiation,[status(thm)],[c_205]) ).
tcf(c_140037,plain,
( between(w,y,u)
| ~ between(u,y,w) ),
inference(instantiation,[status(thm)],[c_118362]) ).
tcf(c_179546,plain,
( between(y,w,v)
| ~ between(u,y,w)
| ~ between(u,w,v) ),
inference(instantiation,[status(thm)],[c_123585]) ).
tcf(c_190993,plain,
( between(y,u,v)
| ~ between(w,y,u)
| ~ between(w,u,v) ),
inference(instantiation,[status(thm)],[c_88572]) ).
tcf(c_250413,plain,
( colinear(w,u,v)
| ~ colinear(u,v,w) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_250657,plain,
( between(v,u,x)
| ~ between(y,u,v)
| ~ between(v,y,x)
| ~ between(v,v,x) ),
inference(instantiation,[status(thm)],[c_58567]) ).
tcf(c_290296,plain,
( between(w,v,u)
| ~ between(u,v,w) ),
inference(instantiation,[status(thm)],[c_15883]) ).
tcf(c_290575,plain,
( between(u,x,v)
| between(u,v,x)
| ~ between(u,x,w)
| ~ between(u,v,w) ),
inference(instantiation,[status(thm)],[c_17213]) ).
tcf(c_293525,plain,
( between(w,x,u)
| ~ between(u,v,w)
| ~ equidistant(v,w,x,u)
| ~ equidistant(u,w,w,u)
| ~ equidistant(u,v,w,x) ),
inference(instantiation,[status(thm)],[c_17599]) ).
tcf(c_296125,plain,
( between(u,v,w)
| ~ between(x,w,v)
| ~ equidistant(x,w,u,v)
| ~ equidistant(x,v,u,w)
| ~ equidistant(w,v,v,w) ),
inference(instantiation,[status(thm)],[c_26643]) ).
tcf(c_297496,plain,
( between(u,x,w)
| ~ between(w,x,u) ),
inference(instantiation,[status(thm)],[c_15942]) ).
tcf(c_298295,plain,
( between(x,w,v)
| ~ between(y,w,v)
| ~ between(x,y,v) ),
inference(instantiation,[status(thm)],[c_80598]) ).
tcf(c_308676,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(x,u,v)
| ~ between(X2,X0,X1)
| ~ equidistant(X2,X1,x,v)
| ~ equidistant(X2,X0,x,u)
| ~ equidistant(X0,X1,u,v) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_341203,plain,
! [X0: $i] :
( between(x,u,v)
| ~ between(w,v,X0)
| ~ equidistant(w,v,x,u)
| ~ equidistant(w,X0,x,v)
| ~ equidistant(v,X0,u,v) ),
inference(instantiation,[status(thm)],[c_308676]) ).
tcf(c_341204,plain,
( between(x,u,v)
| ~ between(w,v,u)
| ~ equidistant(w,v,x,u)
| ~ equidistant(w,u,x,v)
| ~ equidistant(v,u,u,v) ),
inference(instantiation,[status(thm)],[c_341203]) ).
tcf(c_341205,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_341204,c_298295,c_297496,c_296125,c_293525,c_290575,c_290296,c_250657,c_250413,c_190993,c_179546,c_140037,c_65399,c_62407,c_56224,c_55113,c_50620,c_49421,c_43497,c_15307,c_11998,c_7484,c_7365,c_7131,c_6940,c_6531,c_2817,c_2072,c_1194,c_1193,c_163,c_164,c_165,c_168,c_169,c_166,c_167,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Wed Sep 23 10:42:12 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 70.29/12.06 % SZS status Started for theBenchmark.p
% 70.29/12.06 % SZS status Unsatisfiable for theBenchmark.p
% 70.29/12.06
% 70.29/12.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 70.29/12.06
% 70.29/12.06 % ------ iProver source info
% 70.29/12.06
% 70.29/12.06 % git: date: 2026-07-19 20:42:38 +0200
% 70.29/12.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 70.29/12.06 % git: non_committed_changes: false
% 70.29/12.06
% 70.29/12.06 % ------ Parsing...% successful
% 70.29/12.06
% 70.29/12.06
% 70.29/12.06 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 70.29/12.06 %
% 70.29/12.06
% 70.29/12.06 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 70.29/12.06
% 70.29/12.06 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 70.29/12.06 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 70.29/12.06 %
% 70.29/12.06
% 70.29/12.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 70.29/12.06 % ------ Proving...
% 70.29/12.06 % ------ Problem Properties
% 70.29/12.06
% 70.29/12.06 %
% 70.29/12.06 % clauses 71
% 70.29/12.06 % conjectures 1
% 70.29/12.06 % EPR 71
% 70.29/12.06 % Horn 54
% 70.29/12.06 % unary 16
% 70.29/12.06 % binary 22
% 70.29/12.06 % lits 207
% 70.29/12.06 % lits eq 24
% 70.29/12.06 % fd_pure 0
% 70.29/12.06 % fd_pseudo 0
% 70.29/12.06 % fd_cond 0
% 70.29/12.06 % fd_pseudo_cond 20
% 70.29/12.06 % AC symbols 0
% 70.29/12.06
% 70.29/12.06 % ------ Schedule EPR non Horn eq is on
% 70.29/12.06
% 70.29/12.06 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 70.29/12.06
% 70.29/12.06
% 70.29/12.06 % ------
% 70.29/12.06 % Current options:
% 70.29/12.06 % ------
% 70.29/12.06
% 70.29/12.06
% 70.29/12.06 %
% 70.29/12.06
% 70.29/12.06 % ------ Proving...
% 70.29/12.06 %
% 70.29/12.06
% 70.29/12.06 % SZS status Unsatisfiable for theBenchmark.p
% 70.29/12.06
% 70.29/12.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 70.29/12.07
% 70.29/12.07
%------------------------------------------------------------------------------