%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO009-3 : 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 : 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 : Fri Sep 25 01:19:31 PM UTC 2026
% Result : Unsatisfiable 62.90s 10.17s
% Output : CNFRefutation 62.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 126 ( 43 unt; 0 def)
% Number of atoms : 309 ( 88 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 343 ( 160 ~; 183 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 220 ( 0 sgn 220 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X2,X3,X0,X1] : insertion(X0,X1,X2,X3) = extension(extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-3.ax',insertion) ).
fof(f32,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| X0 != extension(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
fof(f33,plain,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| extension(X1,X2,X3,X4) != X0 ),
inference(reorient_equations,[],[f32]) ).
fof(f52,axiom,
! [X0,X1] : between(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f54,axiom,
! [X2,X0,X1] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f55,axiom,
! [X0,X1] : between(X0,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
fof(f56,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f57,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
fof(f61,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(f62,axiom,
! [X2,X3,X0,X1] :
( X1 = X2
| between(X0,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
fof(f63,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(f64,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(f65,axiom,
! [X2,X3,X0,X1] :
( between(X0,X1,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
fof(f69,axiom,
! [X0,X1] : X0 != extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
fof(f70,plain,
! [X0,X1] : extension(X1,X0,lower_dimension_point_1,lower_dimension_point_2) != X0,
inference(reorient_equations,[],[f69]) ).
fof(f82,axiom,
! [X2,X0,X1] :
( X1 = insertion(X0,X2,X0,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).
fof(f83,plain,
! [X2,X0,X1] :
( insertion(X0,X2,X0,X1) = X1
| ~ between(X0,X1,X2) ),
inference(reorient_equations,[],[f82]) ).
fof(f87,axiom,
! [X2,X3,X0,X1] :
( between(X1,X3,X2)
| between(X1,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b13) ).
fof(f88,axiom,
! [X2,X3,X0,X1] :
( between(X3,X0,X1)
| between(X0,X3,X1)
| X1 = X2
| ~ between(X3,X1,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).
fof(f89,axiom,
between(a,c,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_e) ).
fof(f90,axiom,
between(a,d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_between_a_and_e) ).
fof(f91,axiom,
~ between(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_between_a_and_d) ).
fof(f92,negated_conjecture,
~ between(a,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_between_a_and_c) ).
fof(f103,plain,
! [X2,X0,X1] :
( extension(extension(X2,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1) = X1
| ~ between(X0,X1,X2) ),
inference(definition_unfolding,[],[f83,f20]) ).
fof(f105,plain,
! [X2,X3,X1,X4] : between(X1,X2,extension(X1,X2,X3,X4)),
inference(equality_resolution,[],[f33]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f105]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] : between(X0,X0,X1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X1,X2)
| ( X0 = X1 )
| ~ between(X3,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_184,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,[],[f63]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X1,X2)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X0,X1,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] : extension(X0,X1,lower_dimension_point_1,lower_dimension_point_2) != X1,
inference(cnf_transformation,[],[f70]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( extension(extension(X2,X0,lower_dimension_point_1,lower_dimension_point_2),X0,X0,X1) = X1 )
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X1,X3,X2)
| between(X1,X2,X3)
| ( X0 = X1 )
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X0,X1)
| between(X0,X3,X1)
| ( X1 = X2 )
| ~ between(X3,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_208,plain,
between(a,c,e),
inference(cnf_transformation,[],[f89]) ).
tcf(c_209,plain,
between(a,d,e),
inference(cnf_transformation,[],[f90]) ).
tcf(c_210,plain,
~ between(a,c,d),
inference(cnf_transformation,[],[f91]) ).
tcf(c_211,negated_conjecture,
~ between(a,d,c),
inference(cnf_transformation,[],[f92]) ).
tcf(c_1756,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( between(X0,X2,X4)
| ~ between(X1,X3,X5)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2655,plain,
! [X0: $i] :
( between(a,c,d)
| ~ between(X0,c,d)
| ~ between(X0,a,c) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_2670,plain,
! [X0: $i] :
( between(a,c,d)
| ~ between(a,c,X0)
| ~ between(a,X0,d) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_2672,plain,
! [X0: $i] :
( between(a,d,c)
| ~ between(a,d,X0)
| ~ between(a,X0,c) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_2680,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(a,d,c)
| ~ between(X0,X2,X1)
| ( d != X2 )
| ( c != X1 )
| ( a != X0 ) ),
inference(instantiation,[status(thm)],[c_1761]) ).
tcf(c_2731,plain,
between(e,c,a),
inference(superposition,[status(thm)],[c_208,c_176]) ).
tcf(c_2968,plain,
! [X0: $i] :
( between(c,a,X0)
| ~ between(e,a,X0) ),
inference(superposition,[status(thm)],[c_2731,c_182]) ).
tcf(c_3214,plain,
between(d,d,c),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_3377,plain,
! [X0: $i] :
( between(a,d,X0)
| ~ between(X0,d,a) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_3524,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X0,d)
| between(X0,X2,d)
| ( d = X1 )
| ~ between(X2,d,X1)
| ~ between(X0,d,X1) ),
inference(instantiation,[status(thm)],[c_207]) ).
tcf(c_3532,plain,
! [X0: $i,X1: $i] :
( between(a,d,c)
| ~ between(X0,d,X1)
| ( d != d )
| ( c != X1 )
| ( a != X0 ) ),
inference(instantiation,[status(thm)],[c_2680]) ).
tcf(c_3533,plain,
d = d,
inference(instantiation,[status(thm)],[c_1756]) ).
tcf(c_3576,plain,
between(e,c,a),
inference(resolution,[status(thm)],[c_176,c_208]) ).
tcf(c_3577,plain,
between(e,d,a),
inference(resolution,[status(thm)],[c_176,c_209]) ).
tcf(c_3864,plain,
! [X0: $i] :
( between(X0,c,e)
| ~ between(a,X0,c) ),
inference(resolution,[status(thm)],[c_182,c_208]) ).
tcf(c_3871,plain,
! [X0: $i] :
( between(X0,d,a)
| ~ between(e,X0,d) ),
inference(resolution,[status(thm)],[c_182,c_3577]) ).
tcf(c_3964,plain,
between(c,c,e),
inference(resolution,[status(thm)],[c_3864,c_174]) ).
tcf(c_4071,plain,
( between(a,c,d)
| ~ between(c,c,d)
| ~ between(c,a,c) ),
inference(instantiation,[status(thm)],[c_2655]) ).
tcf(c_4072,plain,
between(c,c,d),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_4350,plain,
! [X0: $i] :
( between(e,X0,a)
| ~ between(c,X0,a) ),
inference(resolution,[status(thm)],[c_185,c_3576]) ).
tcf(c_4435,plain,
! [X0: $i] :
( ( a = X0 )
| ~ between(e,a,X0)
| ~ between(c,X0,a) ),
inference(resolution,[status(thm)],[c_4350,c_179]) ).
tcf(c_6129,plain,
( ( a = a )
| ~ between(c,a,a) ),
inference(resolution,[status(thm)],[c_4435,c_174]) ).
tcf(c_6409,plain,
! [X0: $i] :
( between(a,e,X0)
| ( c = e )
| ~ between(c,e,X0) ),
inference(resolution,[status(thm)],[c_183,c_208]) ).
tcf(c_6416,plain,
! [X0: $i] :
( between(e,a,X0)
| ( d = a )
| ~ between(d,a,X0) ),
inference(resolution,[status(thm)],[c_183,c_3577]) ).
tcf(c_6467,plain,
! [X0: $i] :
( between(X0,d,e)
| ( a = d )
| ~ between(X0,a,d) ),
inference(superposition,[status(thm)],[c_209,c_183]) ).
tcf(c_6600,plain,
! [X0: $i] :
( between(e,c,X0)
| ( c = a )
| ~ between(c,a,X0) ),
inference(resolution,[status(thm)],[c_184,c_3576]) ).
tcf(c_6663,plain,
! [X0: $i] :
( between(X0,a,e)
| ( a = d )
| ~ between(X0,a,d) ),
inference(superposition,[status(thm)],[c_209,c_184]) ).
tcf(c_8949,plain,
between(a,a,c),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_8996,plain,
between(c,a,a),
inference(instantiation,[status(thm)],[c_174]) ).
tcf(c_9594,plain,
! [X0: $i] :
( between(a,d,c)
| ~ between(d,d,X0)
| ( d != d )
| ( c != X0 )
| ( a != d ) ),
inference(instantiation,[status(thm)],[c_3532]) ).
tcf(c_9599,plain,
( between(a,d,c)
| ~ between(a,d,e)
| ( d != d )
| ( c != e )
| ( a != a ) ),
inference(instantiation,[status(thm)],[c_3532]) ).
tcf(c_10093,plain,
c = c,
inference(instantiation,[status(thm)],[c_1756]) ).
tcf(c_10204,plain,
! [X0: $i,X1: $i] :
( between(d,X1,X0)
| ~ between(X0,X1,d) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_10615,plain,
! [X0: $i] :
( ( c = e )
| ( c = a )
| ~ between(c,e,X0)
| ~ between(c,a,X0) ),
inference(resolution,[status(thm)],[c_6600,c_178]) ).
tcf(c_10721,plain,
! [X0: $i] :
( between(a,X0,d)
| between(X0,a,d)
| ( d = e )
| ~ between(a,d,e)
| ~ between(X0,d,e) ),
inference(instantiation,[status(thm)],[c_3524]) ).
tcf(c_10894,plain,
! [X0: $i,X1: $i] :
( between(X1,X0,d)
| ~ between(d,X0,X1) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_10952,plain,
! [X0: $i] :
( between(a,X0,c)
| between(X0,a,c)
| ( c = e )
| ~ between(X0,c,e) ),
inference(superposition,[status(thm)],[c_208,c_207]) ).
tcf(c_11163,plain,
! [X0: $i,X1: $i] :
( between(X1,a,c)
| ~ between(X0,a,c)
| ~ between(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_11164,plain,
! [X0: $i] :
( between(X0,a,c)
| ~ between(c,a,X0) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_11310,plain,
! [X0: $i,X1: $i] :
( between(X1,X0,a)
| ~ between(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_11799,plain,
! [X0: $i] :
( between(c,e,X0)
| between(c,X0,e)
| ( a = c )
| ~ between(a,c,X0) ),
inference(resolution,[status(thm)],[c_206,c_208]) ).
tcf(c_17144,plain,
! [X0: $i,X1: $i] :
( between(a,d,c)
| ~ between(X0,a,X1)
| ( d != a )
| ( c != X1 )
| ( a != X0 ) ),
inference(instantiation,[status(thm)],[c_2680]) ).
tcf(c_17473,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X0,X1,X2)
| ( X2 != e )
| ( X1 != c )
| ( X0 != a ) ),
inference(resolution,[status(thm)],[c_1761,c_208]) ).
tcf(c_17474,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X0,X1,X2)
| ( X2 != e )
| ( X1 != d )
| ( X0 != a ) ),
inference(resolution,[status(thm)],[c_1761,c_209]) ).
tcf(c_19122,plain,
( between(a,d,c)
| ~ between(d,d,c)
| ( d != d )
| ( c != c )
| ( a != d ) ),
inference(instantiation,[status(thm)],[c_9594]) ).
tcf(c_21647,plain,
! [X0: $i] :
( between(d,a,X0)
| ~ between(X0,a,d) ),
inference(instantiation,[status(thm)],[c_10204]) ).
tcf(c_24899,plain,
! [X0: $i] :
( between(X0,c,a)
| ~ between(a,c,X0) ),
inference(instantiation,[status(thm)],[c_11310]) ).
tcf(c_26544,plain,
( between(a,d,c)
| ~ between(a,a,c)
| ( d != a )
| ( c != c )
| ( a != a ) ),
inference(instantiation,[status(thm)],[c_17144]) ).
tcf(c_51680,plain,
! [X0: $i] :
( between(c,X0,e)
| between(a,e,X0)
| ( c = e )
| ( a = c )
| ~ between(a,c,X0) ),
inference(resolution,[status(thm)],[c_11799,c_6409]) ).
tcf(c_69215,plain,
! [X0: $i] :
( between(e,X0,d)
| ~ between(d,X0,e) ),
inference(instantiation,[status(thm)],[c_10894]) ).
tcf(c_70959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(extension(X0,X1,X2,X3),X1,X0),
inference(superposition,[status(thm)],[c_160,c_176]) ).
tcf(c_71264,plain,
! [X0: $i] :
( between(c,e,X0)
| ~ between(a,e,X0) ),
inference(superposition,[status(thm)],[c_208,c_182]) ).
tcf(c_75597,plain,
! [X0: $i] :
( between(X0,d,e)
| ~ between(X0,a,d) ),
inference(global_subsumption_just,[status(thm)],[c_6467,c_211,c_3214,c_3533,c_6467,c_10093,c_19122]) ).
tcf(c_75602,plain,
! [X0: $i,X1: $i] : between(extension(d,a,X0,X1),d,e),
inference(superposition,[status(thm)],[c_70959,c_75597]) ).
tcf(c_75714,plain,
! [X0: $i,X1: $i] : between(e,d,extension(d,a,X0,X1)),
inference(superposition,[status(thm)],[c_75602,c_176]) ).
tcf(c_75748,plain,
! [X0: $i,X1: $i] : extension(extension(extension(d,a,X0,X1),e,lower_dimension_point_1,lower_dimension_point_2),e,e,d) = d,
inference(superposition,[status(thm)],[c_75714,c_202]) ).
tcf(c_75997,plain,
! [X0: $i,X1: $i] : between(d,e,extension(extension(d,a,X0,X1),e,lower_dimension_point_1,lower_dimension_point_2)),
inference(superposition,[status(thm)],[c_75748,c_70959]) ).
tcf(c_76198,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(d,X0,e)
| between(X0,d,e)
| ( extension(extension(d,a,X1,X2),e,lower_dimension_point_1,lower_dimension_point_2) = e )
| ~ between(X0,e,extension(extension(d,a,X1,X2),e,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(superposition,[status(thm)],[c_75997,c_207]) ).
tcf(c_76212,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(d,X0,e)
| between(X0,d,e)
| ~ between(X0,e,extension(extension(d,a,X1,X2),e,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76198,c_190]) ).
tcf(c_76739,plain,
! [X0: $i] :
( between(X0,a,e)
| ~ between(X0,a,d) ),
inference(global_subsumption_just,[status(thm)],[c_6663,c_211,c_3214,c_3533,c_6663,c_10093,c_19122]) ).
tcf(c_76744,plain,
! [X0: $i,X1: $i] : between(extension(d,a,X0,X1),a,e),
inference(superposition,[status(thm)],[c_70959,c_76739]) ).
tcf(c_76771,plain,
! [X0: $i,X1: $i] : between(e,a,extension(d,a,X0,X1)),
inference(superposition,[status(thm)],[c_76744,c_176]) ).
tcf(c_76785,plain,
! [X0: $i,X1: $i] : extension(extension(extension(d,a,X0,X1),e,lower_dimension_point_1,lower_dimension_point_2),e,e,a) = a,
inference(superposition,[status(thm)],[c_76771,c_202]) ).
tcf(c_76991,plain,
! [X0: $i,X1: $i] : between(a,e,extension(extension(d,a,X0,X1),e,lower_dimension_point_1,lower_dimension_point_2)),
inference(superposition,[status(thm)],[c_76785,c_70959]) ).
tcf(c_77573,plain,
! [X0: $i,X1: $i] : between(c,e,extension(extension(d,a,X0,X1),e,lower_dimension_point_1,lower_dimension_point_2)),
inference(superposition,[status(thm)],[c_76991,c_71264]) ).
tcf(c_78473,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X0,e,extension(extension(d,a,X1,X2),e,lower_dimension_point_1,lower_dimension_point_2))
| ( c = e )
| ~ between(X0,c,e) ),
inference(superposition,[status(thm)],[c_77573,c_183]) ).
tcf(c_83694,plain,
( ( d != e )
| ( c != c )
| ( a != a ) ),
inference(resolution,[status(thm)],[c_17473,c_210]) ).
tcf(c_83695,plain,
d != e,
inference(equality_resolution_simp,[status(thm)],[c_83694]) ).
tcf(c_86890,plain,
( ( d != d )
| ( c != e )
| ( a != a ) ),
inference(resolution,[status(thm)],[c_17474,c_211]) ).
tcf(c_86891,plain,
c != e,
inference(equality_resolution_simp,[status(thm)],[c_86890]) ).
tcf(c_87919,plain,
! [X0: $i] :
( between(c,X0,e)
| between(a,e,X0)
| ( a = c )
| ~ between(a,c,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51680,c_86891]) ).
tcf(c_87924,plain,
! [X0: $i] :
( ( c = a )
| ~ between(c,e,X0)
| ~ between(c,a,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_10615,c_86891]) ).
tcf(c_88026,plain,
! [X0: $i] :
( between(c,X0,e)
| ( c = a )
| ( a = c )
| ~ between(c,a,X0)
| ~ between(a,c,X0) ),
inference(resolution,[status(thm)],[c_87924,c_11799]) ).
tcf(c_88057,plain,
! [X0: $i] :
( between(a,e,X0)
| ( a = c )
| ( X0 = c )
| ~ between(a,c,X0)
| ~ between(X0,c,e) ),
inference(resolution,[status(thm)],[c_87919,c_178]) ).
tcf(c_101003,plain,
! [X0: $i] :
( between(c,a,c)
| ~ between(X0,c,a)
| ~ between(X0,a,c) ),
inference(instantiation,[status(thm)],[c_11163]) ).
tcf(c_110502,plain,
! [X0: $i] :
( ~ between(a,c,X0)
| ~ between(c,a,X0) ),
inference(global_subsumption_just,[status(thm)],[c_88026,c_210,c_4071,c_4072,c_11164,c_24899,c_101003]) ).
tcf(c_110503,plain,
! [X0: $i] :
( ~ between(c,a,X0)
| ~ between(a,c,X0) ),
inference(renaming,[status(thm)],[c_110502]) ).
tcf(c_116578,plain,
! [X0: $i] :
( ~ between(X0,c,e)
| ~ between(a,c,X0) ),
inference(global_subsumption_just,[status(thm)],[c_88057,c_209,c_211,c_210,c_2670,c_2672,c_2968,c_3377,c_3533,c_3871,c_4071,c_4072,c_6129,c_6416,c_8949,c_8996,c_9599,c_10093,c_10721,c_10952,c_21647,c_24899,c_26544,c_69215,c_76212,c_78473,c_83695,c_101003,c_110503]) ).
tcf(c_116579,plain,
! [X0: $i] :
( ~ between(a,c,X0)
| ~ between(X0,c,e) ),
inference(renaming,[status(thm)],[c_116578]) ).
tcf(c_116610,plain,
~ between(c,c,e),
inference(resolution,[status(thm)],[c_116579,c_174]) ).
tcf(c_116611,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116610,c_3964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO009-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Wed Sep 23 10:19:21 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.34
% 0.07/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.34
% 0.07/0.34 % Detected problem language: tptp
% 0.07/0.35 % Proving...
% 62.90/10.17 % SZS status Started for theBenchmark.p
% 62.90/10.17 % SZS status Unsatisfiable for theBenchmark.p
% 62.90/10.17
% 62.90/10.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 62.90/10.17
% 62.90/10.17 % ------ iProver source info
% 62.90/10.17
% 62.90/10.17 % git: date: 2026-07-19 20:42:38 +0200
% 62.90/10.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 62.90/10.17 % git: non_committed_changes: false
% 62.90/10.17
% 62.90/10.17 % ------ Parsing...% successful
% 62.90/10.17
% 62.90/10.17
% 62.90/10.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 62.90/10.17
% 62.90/10.17 % ------ Preprocessing... sup_sim: 1 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 %
% 62.90/10.17
% 62.90/10.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 62.90/10.17
% 62.90/10.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 62.90/10.17 % ------ Proving...
% 62.90/10.17 % ------ Problem Properties
% 62.90/10.17
% 62.90/10.17 %
% 62.90/10.17 % clauses 71
% 62.90/10.17 % conjectures 1
% 62.90/10.17 % EPR 48
% 62.90/10.17 % Horn 55
% 62.90/10.17 % unary 22
% 62.90/10.17 % binary 15
% 62.90/10.17 % lits 199
% 62.90/10.17 % lits eq 35
% 62.90/10.17 % fd_pure 0
% 62.90/10.17 % fd_pseudo 0
% 62.90/10.17 % fd_cond 0
% 62.90/10.17 % fd_pseudo_cond 20
% 62.90/10.17 % AC symbols 0
% 62.90/10.17
% 62.90/10.17 % ------ Input Options Time Limit: Unbounded
% 62.90/10.17
% 62.90/10.17
% 62.90/10.17 % ------
% 62.90/10.17 % Current options:
% 62.90/10.17 % ------
% 62.90/10.17
% 62.90/10.17
% 62.90/10.17 %
% 62.90/10.17
% 62.90/10.17 % ------ Proving...
% 62.90/10.17 %
% 62.90/10.17
% 62.90/10.17 % SZS status Unsatisfiable for theBenchmark.p
% 62.90/10.17
% 62.90/10.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.90/10.17
% 62.90/10.17
%------------------------------------------------------------------------------