%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:19:30 PM UTC 2026
% Result : Unsatisfiable 1.20s 1.45s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 87 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 45 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( between(X0,X3,X2)
| between(X0,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
fof(f21,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
fof(f22,axiom,
a != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_d) ).
fof(f23,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
fof(f24,axiom,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f25,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X0,X1)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X0,X3,X2)
| between(X0,X2,X3)
| ( X0 = X1 )
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,plain,
a != c,
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,plain,
a != d,
inference(cnf_transformation,[],[f22]) ).
tcf(c_96,plain,
c != d,
inference(cnf_transformation,[],[f23]) ).
tcf(c_97,plain,
between(a,c,d),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_608,plain,
~ between(a,c,a),
inference(resolution,[status(thm)],[c_74,c_94]) ).
tcf(c_610,plain,
~ between(c,d,c),
inference(resolution,[status(thm)],[c_74,c_96]) ).
tcf(c_640,plain,
! [X0: $i] :
( between(a,c,X0)
| ~ between(a,c,d)
| ~ between(c,X0,d) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_641,plain,
( between(a,c,a)
| ~ between(c,a,d)
| ~ between(a,c,d) ),
inference(instantiation,[status(thm)],[c_640]) ).
tcf(c_684,negated_conjecture,
between(a,d,c),
inference(global_subsumption_just,[status(thm)],[c_98,c_97,c_98,c_608,c_641]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( outer_pasch(X1,X0,X0,X3,X2) = X0 )
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_80,c_74]) ).
tcf(c_818,plain,
! [X0: $i] :
( between(a,c,X0)
| between(a,X0,c)
| ( a = d )
| ~ between(a,d,X0) ),
inference(superposition,[status(thm)],[c_684,c_76]) ).
tcf(c_901,negated_conjecture,
between(a,d,c),
inference(global_subsumption_just,[status(thm)],[c_98,c_97,c_98,c_608,c_641]) ).
tcf(c_903,plain,
! [X0: $i] :
( between(a,c,X0)
| between(a,X0,c)
| ~ between(a,d,X0) ),
inference(global_subsumption_just,[status(thm)],[c_818,c_95,c_818]) ).
tcf(c_905,plain,
between(a,c,c),
inference(superposition,[status(thm)],[c_901,c_903]) ).
tcf(c_1333,plain,
! [X0: $i] :
( ( outer_pasch(d,a,a,X0,c) = a )
| ~ between(a,c,X0) ),
inference(superposition,[status(thm)],[c_901,c_800]) ).
tcf(c_1339,plain,
! [X0: $i] :
( ( outer_pasch(c,a,a,X0,c) = a )
| ~ between(a,c,X0) ),
inference(superposition,[status(thm)],[c_905,c_800]) ).
tcf(c_1428,plain,
! [X0: $i] :
( ~ between(d,c,X0)
| ~ between(c,d,X0) ),
inference(resolution,[status(thm)],[c_75,c_610]) ).
tcf(c_1429,plain,
( ~ between(d,c,a)
| ~ between(c,d,a) ),
inference(instantiation,[status(thm)],[c_1428]) ).
tcf(c_1463,negated_conjecture,
between(a,d,c),
inference(global_subsumption_just,[status(thm)],[c_98,c_97,c_98,c_608,c_641]) ).
tcf(c_1465,plain,
! [X0: $i] :
( between(a,c,X0)
| between(a,X0,c)
| ~ between(a,d,X0) ),
inference(global_subsumption_just,[status(thm)],[c_818,c_903]) ).
tcf(c_1467,plain,
between(a,c,c),
inference(superposition,[status(thm)],[c_1463,c_1465]) ).
tcf(c_1468,plain,
outer_pasch(d,a,a,c,c) = a,
inference(superposition,[status(thm)],[c_1467,c_1333]) ).
tcf(c_1470,plain,
outer_pasch(c,a,a,d,c) = a,
inference(superposition,[status(thm)],[c_97,c_1339]) ).
tcf(c_1903,plain,
( between(c,d,a)
| ~ between(a,d,c)
| ~ between(a,c,c) ),
inference(superposition,[status(thm)],[c_1468,c_81]) ).
tcf(c_1905,plain,
( between(d,c,a)
| ~ between(a,c,d)
| ~ between(a,c,c) ),
inference(superposition,[status(thm)],[c_1470,c_81]) ).
tcf(c_1919,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1903,c_1905,c_1429,c_905,c_641,c_608,c_98,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Wed Sep 23 10:17:19 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.53 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 1.20/1.45 % SZS status Started for theBenchmark.p
% 1.20/1.45 % SZS status Unsatisfiable for theBenchmark.p
% 1.20/1.45
% 1.20/1.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.20/1.45
% 1.20/1.45 % ------ iProver source info
% 1.20/1.45
% 1.20/1.45 % git: date: 2026-07-19 20:42:38 +0200
% 1.20/1.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.20/1.45 % git: non_committed_changes: false
% 1.20/1.45
% 1.20/1.45 % ------ Parsing...% successful
% 1.20/1.45
% 1.20/1.45
% 1.20/1.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.20/1.45
% 1.20/1.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.20/1.45
% 1.20/1.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.20/1.45
% 1.20/1.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.20/1.45 % ------ Proving...
% 1.20/1.45 % ------ Problem Properties
% 1.20/1.45
% 1.20/1.45 %
% 1.20/1.45 % clauses 25
% 1.20/1.45 % conjectures 1
% 1.20/1.45 % EPR 16
% 1.20/1.45 % Horn 18
% 1.20/1.45 % unary 10
% 1.20/1.45 % binary 3
% 1.20/1.45 % lits 70
% 1.20/1.45 % lits eq 11
% 1.20/1.45 % fd_pure 0
% 1.20/1.45 % fd_pseudo 0
% 1.20/1.45 % fd_cond 0
% 1.20/1.45 % fd_pseudo_cond 8
% 1.20/1.45 % AC symbols 0
% 1.20/1.45
% 1.20/1.45 % ------ Input Options Time Limit: Unbounded
% 1.20/1.45
% 1.20/1.45
% 1.20/1.45 % ------
% 1.20/1.45 % Current options:
% 1.20/1.45 % ------
% 1.20/1.45
% 1.20/1.45
% 1.20/1.45 %
% 1.20/1.45
% 1.20/1.45 % ------ Proving...
% 1.20/1.45 %
% 1.20/1.45
% 1.20/1.45 % SZS status Unsatisfiable for theBenchmark.p
% 1.20/1.45
% 1.20/1.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.20/1.46
% 1.20/1.46
%------------------------------------------------------------------------------