%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 01:19:44 PM UTC 2026
% Result : Unsatisfiable 2.95s 1.24s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 15 unt; 2 def)
% Number of atoms : 49 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax',reflection) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
fof(f48,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f54,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(definition_unfolding,[],[f48,f19,f19]) ).
tcf(c_92,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_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_131,negated_conjecture,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_888,definition,
iPr_def_10 = extension(u,v,u,v),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_889,definition,
iPr_def_11 = extension(iPr_def_10,v,iPr_def_10,v),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_890,negated_conjecture,
~ equidistant(v,u,v,iPr_def_11),
inference(demodulation,[status(thm)],[c_131,c_888,c_889]) ).
tcf(c_1392,plain,
equidistant(v,iPr_def_10,u,v),
inference(superposition,[status(thm)],[c_888,c_95]) ).
tcf(c_1393,plain,
equidistant(v,iPr_def_11,iPr_def_10,v),
inference(superposition,[status(thm)],[c_889,c_95]) ).
tcf(c_1424,plain,
equidistant(iPr_def_10,v,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1393,c_110]) ).
tcf(c_1472,plain,
equidistant(v,iPr_def_10,iPr_def_11,v),
inference(superposition,[status(thm)],[c_1424,c_113]) ).
tcf(c_1648,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_1392,c_92]) ).
tcf(c_1725,plain,
( equidistant(v,u,v,iPr_def_11)
| ~ equidistant(u,v,iPr_def_11,v) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1863,plain,
equidistant(u,v,iPr_def_11,v),
inference(superposition,[status(thm)],[c_1472,c_1648]) ).
tcf(c_1864,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1863,c_1725,c_890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.33 % Computer : n008.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Wed Sep 23 10:38:39 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 Running first-order theorem proving
% 0.11/0.36 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
% 0.11/0.37
% 0.11/0.37 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.37
% 0.11/0.37 % Detected problem language: tptp
% 0.11/0.39 % Proving...
% 2.95/1.24 % SZS status Started for theBenchmark.p
% 2.95/1.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.95/1.24
% 2.95/1.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.95/1.24
% 2.95/1.24 % ------ iProver source info
% 2.95/1.24
% 2.95/1.24 % git: date: 2026-07-19 20:42:38 +0200
% 2.95/1.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.95/1.24 % git: non_committed_changes: false
% 2.95/1.24
% 2.95/1.24 % ------ Parsing...% successful
% 2.95/1.24
% 2.95/1.24
% 2.95/1.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.95/1.24
% 2.95/1.24 % ------ Preprocessing... sup_sim: 0 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 %
% 2.95/1.24
% 2.95/1.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.95/1.24
% 2.95/1.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.95/1.24 % ------ Proving...
% 2.95/1.24 % ------ Problem Properties
% 2.95/1.24
% 2.95/1.24 %
% 2.95/1.24 % clauses 38
% 2.95/1.24 % conjectures 1
% 2.95/1.24 % EPR 22
% 2.95/1.24 % Horn 29
% 2.95/1.24 % unary 12
% 2.95/1.24 % binary 11
% 2.95/1.24 % lits 99
% 2.95/1.24 % lits eq 20
% 2.95/1.24 % fd_pure 0
% 2.95/1.24 % fd_pseudo 0
% 2.95/1.24 % fd_cond 0
% 2.95/1.24 % fd_pseudo_cond 11
% 2.95/1.24 % AC symbols 0
% 2.95/1.24
% 2.95/1.24 % ------ Schedule dynamic 5 is on
% 2.95/1.24
% 2.95/1.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.95/1.24
% 2.95/1.24
% 2.95/1.24 % ------
% 2.95/1.24 % Current options:
% 2.95/1.24 % ------
% 2.95/1.24
% 2.95/1.24
% 2.95/1.24 %
% 2.95/1.24
% 2.95/1.24 % ------ Proving...
% 2.95/1.24 %
% 2.95/1.24
% 2.95/1.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.95/1.24
% 2.95/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.95/1.24
% 2.95/1.24
%------------------------------------------------------------------------------