%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO059-2 : 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 : n019.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 01:19:43 PM UTC 2026
% Result : Unsatisfiable 2.71s 1.28s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 19 unt; 2 def)
% Number of atoms : 53 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 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 : 46 ( 0 sgn 46 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/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/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(f20,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_congruence) ).
fof(f21,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(definition_unfolding,[],[f20,f19,f19]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,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_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,negated_conjecture,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_315,definition,
iPr_def_10 = extension(u,v,u,v),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_316,definition,
iPr_def_11 = extension(iPr_def_10,v,iPr_def_10,v),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_317,negated_conjecture,
~ equidistant(v,u,v,iPr_def_11),
inference(demodulation,[status(thm)],[c_87,c_315,c_316]) ).
tcf(c_647,plain,
equidistant(v,iPr_def_10,u,v),
inference(superposition,[status(thm)],[c_315,c_73]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(v,iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_647,c_70]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_69,c_664]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(superposition,[status(thm)],[c_690,c_665]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i] :
( equidistant(v,u,v,iPr_def_11)
| ~ equidistant(X0,X1,v,iPr_def_11)
| ~ equidistant(X0,X1,v,u) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_814,plain,
( equidistant(v,u,v,iPr_def_11)
| ~ equidistant(u,v,v,iPr_def_11)
| ~ equidistant(u,v,v,u) ),
inference(instantiation,[status(thm)],[c_757]) ).
tcf(c_815,plain,
equidistant(u,v,v,u),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_861,plain,
equidistant(iPr_def_10,v,v,iPr_def_11),
inference(superposition,[status(thm)],[c_316,c_730]) ).
tcf(c_871,plain,
equidistant(v,iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_861,c_664]) ).
tcf(c_878,plain,
equidistant(u,v,v,iPr_def_11),
inference(superposition,[status(thm)],[c_871,c_670]) ).
tcf(c_881,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_878,c_815,c_814,c_317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 10:38:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.71/1.28 % SZS status Started for theBenchmark.p
% 2.71/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.71/1.28
% 2.71/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.71/1.28
% 2.71/1.28 % ------ iProver source info
% 2.71/1.28
% 2.71/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.71/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.71/1.28 % git: non_committed_changes: false
% 2.71/1.28
% 2.71/1.28 % ------ Parsing...% successful
% 2.71/1.28
% 2.71/1.28
% 2.71/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.71/1.28
% 2.71/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.71/1.28
% 2.71/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.71/1.28
% 2.71/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.71/1.28 % ------ Proving...
% 2.71/1.28 % ------ Problem Properties
% 2.71/1.28
% 2.71/1.28 %
% 2.71/1.28 % clauses 21
% 2.71/1.28 % conjectures 1
% 2.71/1.28 % EPR 10
% 2.71/1.28 % Horn 16
% 2.71/1.28 % unary 9
% 2.71/1.28 % binary 2
% 2.71/1.28 % lits 59
% 2.71/1.28 % lits eq 9
% 2.71/1.28 % fd_pure 0
% 2.71/1.28 % fd_pseudo 0
% 2.71/1.28 % fd_cond 0
% 2.71/1.28 % fd_pseudo_cond 7
% 2.71/1.28 % AC symbols 0
% 2.71/1.28
% 2.71/1.28 % ------ Schedule dynamic 5 is on
% 2.71/1.28
% 2.71/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.71/1.28
% 2.71/1.28
% 2.71/1.28 % ------
% 2.71/1.28 % Current options:
% 2.71/1.28 % ------
% 2.71/1.28
% 2.71/1.28
% 2.71/1.28 %
% 2.71/1.28
% 2.71/1.28 % ------ Proving...
% 2.71/1.28 %
% 2.71/1.28
% 2.71/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.71/1.28
% 2.71/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.71/1.28
% 2.71/1.28
%------------------------------------------------------------------------------