%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:19:29 PM UTC 2026
% Result : Unsatisfiable 4.48s 1.53s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
fof(f2,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f3,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/theBenchmark.p',outer_pasch1) ).
fof(f4,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/theBenchmark.p',outer_pasch2) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( between(X2,X3,X1)
| ~ between(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_substitution3) ).
fof(f8,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,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,[],[f3]) ).
tcf(c_60,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,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
~ between(a,a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] : equalish(X0,extension(X1,X0,X2,X2)),
inference(resolution,[status(thm)],[c_58,c_62]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X0,X1,extension(X3,X2,X4,X4))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_63,c_104]) ).
tcf(c_145,negated_conjecture,
~ between(a,a,b),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X2,X0,X1)
| ~ between(X0,X1,extension(X2,X0,X3,X4)) ),
inference(superposition,[status(thm)],[c_61,c_57]) ).
tcf(c_298,plain,
! [X0: $i] : between(X0,X0,X0),
inference(superposition,[status(thm)],[c_61,c_228]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X0,X1)
| ~ between(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_110,c_228]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_298,c_299]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X4,X0,outer_pasch(X1,X0,X0,X3,X2))
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_59,c_299]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( between(X4,X0,X1)
| ~ between(X3,X5,X4)
| ~ between(X2,X0,X5)
| ~ between(X0,X1,outer_pasch(X0,X2,X3,X4,X5)) ),
inference(superposition,[status(thm)],[c_60,c_57]) ).
tcf(c_1810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X3,X1,X0)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_464,c_590]) ).
tcf(c_1983,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_374,c_1810]) ).
tcf(c_2464,plain,
! [X0: $i,X1: $i] : between(X0,X0,X1),
inference(superposition,[status(thm)],[c_374,c_1983]) ).
tcf(c_2484,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_145,c_2464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 10:22:58 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 4.48/1.53 % SZS status Started for theBenchmark.p
% 4.48/1.53 % SZS status Unsatisfiable for theBenchmark.p
% 4.48/1.53
% 4.48/1.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.48/1.53
% 4.48/1.53 % ------ iProver source info
% 4.48/1.53
% 4.48/1.53 % git: date: 2026-07-19 20:42:38 +0200
% 4.48/1.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.48/1.53 % git: non_committed_changes: false
% 4.48/1.53
% 4.48/1.53 % ------ Parsing...% successful
% 4.48/1.53
% 4.48/1.53
% 4.48/1.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.48/1.53
% 4.48/1.53 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.48/1.53
% 4.48/1.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.48/1.53 % ------ Proving...
% 4.48/1.53 % ------ Problem Properties
% 4.48/1.53
% 4.48/1.53 %
% 4.48/1.53 % clauses 6
% 4.48/1.53 % conjectures 1
% 4.48/1.53 % EPR 2
% 4.48/1.53 % Horn 6
% 4.48/1.53 % unary 2
% 4.48/1.53 % binary 1
% 4.48/1.53 % lits 13
% 4.48/1.53 % lits eq 0
% 4.48/1.53 % fd_pure 0
% 4.48/1.53 % fd_pseudo 0
% 4.48/1.53 % fd_cond 0
% 4.48/1.53 % fd_pseudo_cond 0
% 4.48/1.53 % AC symbols 0
% 4.48/1.53
% 4.48/1.53 % ------ Schedule dynamic 5 is on
% 4.48/1.53
% 4.48/1.53 % ------ no equalities: superposition off
% 4.48/1.53
% 4.48/1.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.48/1.53
% 4.48/1.53
% 4.48/1.53 % ------
% 4.48/1.53 % Current options:
% 4.48/1.53 % ------
% 4.48/1.53
% 4.48/1.53
% 4.48/1.53 %
% 4.48/1.53
% 4.48/1.53 % ------ Proving...
% 4.48/1.53 %
% 4.48/1.53
% 4.48/1.53 % SZS status Unsatisfiable for theBenchmark.p
% 4.48/1.53
% 4.48/1.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.48/1.53
% 4.48/1.53
%------------------------------------------------------------------------------