%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:19:28 PM UTC 2026
% Result : Unsatisfiable 3.81s 1.34s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 41 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
fof(f5,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
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/sandbox/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/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
fof(f13,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
fof(f21,axiom,
between(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_between_a_and_c) ).
fof(f22,negated_conjecture,
~ between(c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_c_and_a) ).
tcf(c_71,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] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_77,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_78,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_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,plain,
between(a,b,c),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
~ between(c,b,a),
inference(cnf_transformation,[],[f22]) ).
tcf(c_354,negated_conjecture,
~ between(c,b,a),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_84,c_75]) ).
tcf(c_721,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_77,c_71]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_701,c_83]) ).
tcf(c_2721,plain,
! [X0: $i] :
( ( outer_pasch(b,a,a,X0,c) = a )
| ~ between(a,c,X0) ),
inference(superposition,[status(thm)],[c_91,c_721]) ).
tcf(c_2795,plain,
outer_pasch(b,a,a,c,c) = a,
inference(superposition,[status(thm)],[c_731,c_2721]) ).
tcf(c_2831,plain,
( between(c,b,a)
| ~ between(a,c,c)
| ~ between(a,b,c) ),
inference(superposition,[status(thm)],[c_2795,c_78]) ).
tcf(c_2835,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2831,c_354,c_731,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.43 % Computer : n009.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Wed Sep 23 10:17:13 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.47 Running first-order theorem proving
% 0.13/0.47 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
% 0.13/0.48
% 0.13/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.48
% 0.13/0.49 % Detected problem language: tptp
% 0.13/0.50 % Proving...
% 3.81/1.34 % SZS status Started for theBenchmark.p
% 3.81/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 3.81/1.34
% 3.81/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.81/1.34
% 3.81/1.34 % ------ iProver source info
% 3.81/1.34
% 3.81/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 3.81/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.81/1.34 % git: non_committed_changes: false
% 3.81/1.34
% 3.81/1.34 % ------ Parsing...% successful
% 3.81/1.34
% 3.81/1.34
% 3.81/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.81/1.34
% 3.81/1.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.81/1.34
% 3.81/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.81/1.34
% 3.81/1.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/1.34 % ------ Proving...
% 3.81/1.34 % ------ Problem Properties
% 3.81/1.34
% 3.81/1.34 %
% 3.81/1.34 % clauses 22
% 3.81/1.34 % conjectures 1
% 3.81/1.34 % EPR 13
% 3.81/1.34 % Horn 16
% 3.81/1.34 % unary 8
% 3.81/1.34 % binary 2
% 3.81/1.34 % lits 66
% 3.81/1.34 % lits eq 8
% 3.81/1.34 % fd_pure 0
% 3.81/1.34 % fd_pseudo 0
% 3.81/1.34 % fd_cond 0
% 3.81/1.34 % fd_pseudo_cond 8
% 3.81/1.34 % AC symbols 0
% 3.81/1.34
% 3.81/1.34 % ------ Schedule dynamic 5 is on
% 3.81/1.34
% 3.81/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/1.34
% 3.81/1.34
% 3.81/1.34 % ------
% 3.81/1.34 % Current options:
% 3.81/1.34 % ------
% 3.81/1.34
% 3.81/1.34
% 3.81/1.34 %
% 3.81/1.34
% 3.81/1.34 % ------ Proving...
% 3.81/1.34 %
% 3.81/1.34
% 3.81/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 3.81/1.34
% 3.81/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/1.34
% 3.81/1.34
%------------------------------------------------------------------------------