%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 2.01s 1.28s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 21 :)
% 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/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
fof(f20,axiom,
v = reflection(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_equals_reflection) ).
fof(f21,negated_conjecture,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_equals_v) ).
fof(f22,plain,
v != u,
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
v = extension(u,v,u,v),
inference(definition_unfolding,[],[f20,f19]) ).
tcf(c_71,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_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_88,plain,
extension(u,v,u,v) = v,
inference(cnf_transformation,[],[f23]) ).
tcf(c_89,negated_conjecture,
v != u,
inference(cnf_transformation,[],[f22]) ).
tcf(c_319,negated_conjecture,
v != u,
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_642,plain,
equidistant(v,v,u,v),
inference(superposition,[status(thm)],[c_88,c_74]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_74,c_72]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( equidistant(u,v,X0,X1)
| ~ equidistant(v,v,X0,X1) ),
inference(superposition,[status(thm)],[c_642,c_71]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] : equidistant(X0,X0,X1,X1),
inference(superposition,[status(thm)],[c_655,c_74]) ).
tcf(c_705,plain,
! [X0: $i] : equidistant(u,v,X0,X0),
inference(superposition,[status(thm)],[c_673,c_668]) ).
tcf(c_710,plain,
v = u,
inference(superposition,[status(thm)],[c_705,c_72]) ).
tcf(c_711,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_710,c_319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:39:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.01/1.28 % SZS status Started for theBenchmark.p
% 2.01/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/1.28
% 2.01/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.01/1.28
% 2.01/1.28 % ------ iProver source info
% 2.01/1.28
% 2.01/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.01/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.01/1.28 % git: non_committed_changes: false
% 2.01/1.28
% 2.01/1.28 % ------ Parsing...% successful
% 2.01/1.28
% 2.01/1.28
% 2.01/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.01/1.28
% 2.01/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.01/1.28
% 2.01/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.01/1.28
% 2.01/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.01/1.28 % ------ Proving...
% 2.01/1.28 % ------ Problem Properties
% 2.01/1.28
% 2.01/1.28 %
% 2.01/1.28 % clauses 20
% 2.01/1.28 % conjectures 1
% 2.01/1.28 % EPR 10
% 2.01/1.28 % Horn 15
% 2.01/1.28 % unary 8
% 2.01/1.28 % binary 2
% 2.01/1.28 % lits 58
% 2.01/1.28 % lits eq 9
% 2.01/1.28 % fd_pure 0
% 2.01/1.28 % fd_pseudo 0
% 2.01/1.28 % fd_cond 0
% 2.01/1.28 % fd_pseudo_cond 7
% 2.01/1.28 % AC symbols 0
% 2.01/1.28
% 2.01/1.28 % ------ Schedule dynamic 5 is on
% 2.01/1.28
% 2.01/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.01/1.28
% 2.01/1.28
% 2.01/1.28 % ------
% 2.01/1.28 % Current options:
% 2.01/1.28 % ------
% 2.01/1.28
% 2.01/1.28
% 2.01/1.28 %
% 2.01/1.28
% 2.01/1.28 % ------ Proving...
% 2.01/1.28 %
% 2.01/1.28
% 2.01/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/1.28
% 2.01/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.01/1.28
% 2.01/1.28
%------------------------------------------------------------------------------