%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 01:19:36 PM UTC 2026
% Result : Unsatisfiable 30.42s 6.82s
% Output : CNFRefutation 30.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 23 unt; 0 def)
% Number of atoms : 109 ( 24 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 125 ( 62 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( 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) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f21,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X1,X4,X3,X5)
| ( X0 = X6 )
| ~ between(X7,X2,X3)
| ~ between(X6,X0,X1)
| ~ equidistant(X6,X4,X7,X5)
| ~ equidistant(X6,X0,X7,X2)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_88,plain,
between(u,v,w),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
u != v,
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
extension(u,v,v,w) != w,
inference(cnf_transformation,[],[f21]) ).
tcf(c_218,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_466,plain,
! [X0: $i] :
( ( u = v )
| ( v != X0 )
| ( u != X0 ) ),
inference(instantiation,[status(thm)],[c_220]) ).
tcf(c_496,plain,
equidistant(v,extension(u,v,v,w),v,w),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_600,plain,
( ( u = v )
| ( v != u )
| ( u != u ) ),
inference(instantiation,[status(thm)],[c_466]) ).
tcf(c_601,plain,
u = u,
inference(instantiation,[status(thm)],[c_218]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i] : equidistant(X0,extension(X1,X0,u,v),u,v),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_937,plain,
equidistant(v,extension(v,v,u,v),u,v),
inference(instantiation,[status(thm)],[c_935]) ).
tcf(c_953,plain,
! [X0: $i,X1: $i,X2: $i] : equidistant(u,extension(X0,u,X1,X2),X1,X2),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_2181,plain,
! [X0: $i] : equidistant(u,extension(X0,u,u,w),u,w),
inference(instantiation,[status(thm)],[c_953]) ).
tcf(c_2932,plain,
! [X0: $i] : equidistant(w,X0,X0,w),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2934,plain,
equidistant(w,v,v,w),
inference(instantiation,[status(thm)],[c_2932]) ).
tcf(c_3028,plain,
! [X0: $i] :
( ( extension(u,v,v,w) = w )
| ~ equidistant(extension(u,v,v,w),w,X0,X0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_3049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(extension(u,v,v,w),w,X2,X2)
| ( X0 = X3 )
| ~ between(X4,X1,X2)
| ~ equidistant(X3,w,X4,X2)
| ~ equidistant(X0,w,X1,X2)
| ~ equidistant(X3,X0,X4,X1)
| ~ between(X3,X0,extension(u,v,v,w))
| ~ equidistant(X0,extension(u,v,v,w),X1,X2) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X4,w,X2,X3)
| ~ equidistant(X0,X1,X4,w)
| ~ equidistant(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_3148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(u,X2,u,X3)
| ~ equidistant(X0,X1,u,X3)
| ~ equidistant(X0,X1,u,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_3589,plain,
between(u,v,extension(u,v,v,w)),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3628,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X0,w,X1,X2)
| ~ equidistant(w,X0,X0,w)
| ~ equidistant(w,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_3142]) ).
tcf(c_3631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(X2,w,X3,X4)
| ~ equidistant(X0,extension(X1,X0,X2,w),X2,w)
| ~ equidistant(X0,extension(X1,X0,X2,w),X3,X4) ),
inference(instantiation,[status(thm)],[c_3142]) ).
tcf(c_3665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(u,X3,u,X2)
| ~ equidistant(X0,extension(X1,X0,u,X2),u,X3)
| ~ equidistant(X0,extension(X1,X0,u,X2),u,X2) ),
inference(instantiation,[status(thm)],[c_3148]) ).
tcf(c_3667,plain,
( equidistant(u,v,u,v)
| ~ equidistant(v,extension(v,v,u,v),u,v) ),
inference(instantiation,[status(thm)],[c_3665]) ).
tcf(c_7371,plain,
! [X0: $i] :
( equidistant(X0,w,X0,w)
| ~ equidistant(w,X0,X0,w) ),
inference(instantiation,[status(thm)],[c_3628]) ).
tcf(c_7372,plain,
( equidistant(v,w,v,w)
| ~ equidistant(w,v,v,w) ),
inference(instantiation,[status(thm)],[c_7371]) ).
tcf(c_7484,plain,
! [X0: $i] :
( equidistant(u,w,u,w)
| ~ equidistant(u,extension(X0,u,u,w),u,w) ),
inference(instantiation,[status(thm)],[c_3631]) ).
tcf(c_7722,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(extension(u,v,v,w),w,X2,X2)
| ( X0 = u )
| ~ between(u,X1,X2)
| ~ equidistant(u,w,u,X2)
| ~ equidistant(u,X0,u,X1)
| ~ equidistant(X0,w,X1,X2)
| ~ between(u,X0,extension(u,v,v,w))
| ~ equidistant(X0,extension(u,v,v,w),X1,X2) ),
inference(instantiation,[status(thm)],[c_3049]) ).
tcf(c_22508,plain,
( ( extension(u,v,v,w) = w )
| ~ equidistant(extension(u,v,v,w),w,w,w) ),
inference(instantiation,[status(thm)],[c_3028]) ).
tcf(c_23421,plain,
( equidistant(extension(u,v,v,w),w,w,w)
| ( v = u )
| ~ between(u,v,w)
| ~ equidistant(v,w,v,w)
| ~ equidistant(u,w,u,w)
| ~ equidistant(u,v,u,v)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,extension(u,v,v,w),v,w) ),
inference(instantiation,[status(thm)],[c_7722]) ).
tcf(c_23422,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23421,c_22508,c_7484,c_7372,c_3667,c_3589,c_2934,c_2181,c_937,c_601,c_600,c_496,c_90,c_89,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 10:27:47 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 30.42/6.82 % SZS status Started for theBenchmark.p
% 30.42/6.82 % SZS status Unsatisfiable for theBenchmark.p
% 30.42/6.82
% 30.42/6.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 30.42/6.82
% 30.42/6.82 % ------ iProver source info
% 30.42/6.82
% 30.42/6.82 % git: date: 2026-07-19 20:42:38 +0200
% 30.42/6.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 30.42/6.82 % git: non_committed_changes: false
% 30.42/6.82
% 30.42/6.82 % ------ Parsing...% successful
% 30.42/6.82
% 30.42/6.82
% 30.42/6.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 30.42/6.82
% 30.42/6.82 % ------ Preprocessing...%
% 30.42/6.82
% 30.42/6.82 % ------ Preprocessing...%
% 30.42/6.82
% 30.42/6.82 % ------ Preprocessing...
% 30.42/6.82 % ------ Proving...
% 30.42/6.82 % ------ Problem Properties
% 30.42/6.82
% 30.42/6.82 %
% 30.42/6.82 % clauses 21
% 30.42/6.82 % conjectures 1
% 30.42/6.82 % EPR 11
% 30.42/6.82 % Horn 16
% 30.42/6.82 % unary 9
% 30.42/6.82 % binary 2
% 30.42/6.82 % lits 59
% 30.42/6.82 % lits eq 9
% 30.42/6.82 % fd_pure 0
% 30.42/6.82 % fd_pseudo 0
% 30.42/6.82 % fd_cond 0
% 30.42/6.82 % fd_pseudo_cond 7
% 30.42/6.82 % AC symbols 0
% 30.42/6.82
% 30.42/6.82 % ------ Input Options Time Limit: Unbounded
% 30.42/6.82
% 30.42/6.82
% 30.42/6.82 % ------
% 30.42/6.82 % Current options:
% 30.42/6.82 % ------
% 30.42/6.82
% 30.42/6.82
% 30.42/6.82 %
% 30.42/6.82
% 30.42/6.82 % ------ Proving...
% 30.42/6.82 %
% 30.42/6.82
% 30.42/6.82 % SZS status Unsatisfiable for theBenchmark.p
% 30.42/6.82
% 30.42/6.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.42/6.82
% 30.42/6.82
%------------------------------------------------------------------------------