%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO053-2 : 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 : 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 01:19:42 PM UTC 2026
% Result : Unsatisfiable 24.52s 4.45s
% Output : CNFRefutation 24.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 120 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 121 ( 58 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 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 : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 175 ( 0 sgn 175 !; 0 ?; 136 :)
% 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(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
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(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
equidistant(u,v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
fof(f21,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_w) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
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_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
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_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X1,X4,X3,X5)
| ( X0 = X6 )
| ~ between(X7,X2,X3)
| ~ between(X6,X0,X1)
| ~ equidistant(X6,X4,X7,X5)
| ~ equidistant(X6,X0,X7,X2)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_88,plain,
between(u,v,w),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
equidistant(u,v,u,w),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
v != w,
inference(cnf_transformation,[],[f21]) ).
tcf(c_1694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_70,c_71]) ).
tcf(c_1698,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_74,c_71]) ).
tcf(c_1699,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_74,c_72]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_1699,c_73]) ).
tcf(c_1710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(v,X1,w,X3)
| ( X0 = u )
| ~ between(X2,u,w)
| ~ between(X0,u,v)
| ~ equidistant(u,X1,u,X3)
| ~ equidistant(X0,u,X2,u)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_89,c_75]) ).
tcf(c_1718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inner_pasch(X0,X1,X2,X3,X1) = X1 )
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_77,c_76]) ).
tcf(c_1722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inner_pasch(X0,X1,X2,X0,X3) = X0 )
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_78,c_76]) ).
tcf(c_1794,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_70,c_1694]) ).
tcf(c_1805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(superposition,[status(thm)],[c_70,c_1698]) ).
tcf(c_1854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inner_pasch(X2,X0,extension(X2,X0,X3,X4),X1,X0) = X0 )
| ~ between(X0,X1,extension(X2,X0,X3,X4)) ),
inference(superposition,[status(thm)],[c_73,c_1718]) ).
tcf(c_1865,plain,
! [X0: $i] :
( ( inner_pasch(u,v,w,u,X0) = u )
| ~ between(X0,u,w) ),
inference(superposition,[status(thm)],[c_88,c_1722]) ).
tcf(c_1872,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inner_pasch(X1,X2,X2,X1,X0) = X1 )
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1700,c_1722]) ).
tcf(c_1978,plain,
! [X0: $i,X1: $i] :
( equidistant(v,X1,w,X1)
| ( X0 = u )
| ~ between(X0,u,w)
| ~ between(X0,u,v)
| ~ equidistant(u,X1,u,X1)
| ~ equidistant(X0,u,X0,u) ),
inference(superposition,[status(thm)],[c_1794,c_1710]) ).
tcf(c_1988,plain,
! [X0: $i,X1: $i] :
( equidistant(v,X1,w,X1)
| ( X0 = u )
| ~ between(X0,u,w)
| ~ between(X0,u,v) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1978,c_1794,c_1794]) ).
tcf(c_2159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : equidistant(X0,X1,extension(X2,X3,X4,extension(X5,X4,X0,X1)),X3),
inference(superposition,[status(thm)],[c_1805,c_1698]) ).
tcf(c_2447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inner_pasch(X0,X1,extension(X0,X1,X2,X3),extension(X0,X1,X2,X3),X1) = X1,
inference(superposition,[status(thm)],[c_1700,c_1854]) ).
tcf(c_2471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(extension(X1,X0,X2,X3),X0,X1)
| ~ between(X1,X0,extension(X1,X0,X2,X3))
| ~ between(X0,extension(X1,X0,X2,X3),extension(X1,X0,X2,X3)) ),
inference(superposition,[status(thm)],[c_2447,c_78]) ).
tcf(c_2473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(extension(X0,X1,X2,X3),X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_2471,c_73,c_1700]) ).
tcf(c_2838,plain,
! [X0: $i,X1: $i] : inner_pasch(u,v,w,u,extension(w,u,X0,X1)) = u,
inference(superposition,[status(thm)],[c_2473,c_1865]) ).
tcf(c_2865,plain,
! [X0: $i,X1: $i] :
( between(v,u,extension(w,u,X0,X1))
| ~ between(u,v,w)
| ~ between(extension(w,u,X0,X1),u,w) ),
inference(superposition,[status(thm)],[c_2838,c_77]) ).
tcf(c_2868,plain,
! [X0: $i,X1: $i] : between(v,u,extension(w,u,X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_2865,c_88,c_2473]) ).
tcf(c_3221,plain,
! [X0: $i,X1: $i] : inner_pasch(u,extension(w,u,X0,X1),extension(w,u,X0,X1),u,v) = u,
inference(superposition,[status(thm)],[c_2868,c_1872]) ).
tcf(c_3280,plain,
! [X0: $i,X1: $i] :
( between(extension(w,u,X0,X1),u,v)
| ~ between(v,u,extension(w,u,X0,X1))
| ~ between(u,extension(w,u,X0,X1),extension(w,u,X0,X1)) ),
inference(superposition,[status(thm)],[c_3221,c_77]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i] : between(extension(w,u,X0,X1),u,v),
inference(forward_subsumption_resolution,[status(thm)],[c_3280,c_2868,c_1700]) ).
tcf(c_4439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : equidistant(X0,X1,extension(X2,X3,X4,extension(X5,X4,X1,X0)),X3),
inference(superposition,[status(thm)],[c_2159,c_1694]) ).
tcf(c_4945,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(v,X2,w,X2)
| ( extension(w,u,X0,X1) = u )
| ~ between(extension(w,u,X0,X1),u,w) ),
inference(superposition,[status(thm)],[c_3283,c_1988]) ).
tcf(c_4946,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(v,X2,w,X2)
| ( extension(w,u,X0,X1) = u ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4945,c_2473]) ).
tcf(c_7391,plain,
! [X0: $i,X1: $i] :
( ( v = w )
| ( extension(w,u,X0,X1) = u ) ),
inference(superposition,[status(thm)],[c_4946,c_72]) ).
tcf(c_7400,plain,
! [X0: $i,X1: $i] : extension(w,u,X0,X1) = u,
inference(forward_subsumption_resolution,[status(thm)],[c_7391,c_90]) ).
tcf(c_7501,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,u,u),
inference(superposition,[status(thm)],[c_7400,c_4439]) ).
tcf(c_8669,plain,
! [X0: $i,X1: $i] : X0 = X1,
inference(superposition,[status(thm)],[c_7501,c_72]) ).
tcf(c_9762,plain,
! [X0: $i] : X0 != w,
inference(superposition,[status(thm)],[c_8669,c_90]) ).
tcf(c_9910,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9762,c_8669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO053-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 10:41:10 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 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
% 0.15/0.50
% 0.15/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.50
% 0.15/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 24.52/4.45 % SZS status Started for theBenchmark.p
% 24.52/4.45 % SZS status Unsatisfiable for theBenchmark.p
% 24.52/4.45
% 24.52/4.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 24.52/4.45
% 24.52/4.45 % ------ iProver source info
% 24.52/4.45
% 24.52/4.45 % git: date: 2026-07-19 20:42:38 +0200
% 24.52/4.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 24.52/4.45 % git: non_committed_changes: false
% 24.52/4.45
% 24.52/4.45 % ------ Parsing...% successful
% 24.52/4.45
% 24.52/4.45
% 24.52/4.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 24.52/4.45
% 24.52/4.45 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 24.52/4.45
% 24.52/4.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 24.52/4.45
% 24.52/4.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.52/4.45 % ------ Proving...
% 24.52/4.45 % ------ Problem Properties
% 24.52/4.45
% 24.52/4.45 %
% 24.52/4.45 % clauses 21
% 24.52/4.45 % conjectures 1
% 24.52/4.45 % EPR 12
% 24.52/4.45 % Horn 16
% 24.52/4.45 % unary 9
% 24.52/4.45 % binary 2
% 24.52/4.45 % lits 59
% 24.52/4.45 % lits eq 8
% 24.52/4.45 % fd_pure 0
% 24.52/4.45 % fd_pseudo 0
% 24.52/4.45 % fd_cond 0
% 24.52/4.45 % fd_pseudo_cond 7
% 24.52/4.45 % AC symbols 0
% 24.52/4.45
% 24.52/4.45 % ------ Input Options Time Limit: Unbounded
% 24.52/4.45
% 24.52/4.45
% 24.52/4.45 % ------
% 24.52/4.45 % Current options:
% 24.52/4.45 % ------
% 24.52/4.45
% 24.52/4.45
% 24.52/4.45 %
% 24.52/4.45
% 24.52/4.45 % ------ Proving...
% 24.52/4.45 %
% 24.52/4.45
% 24.52/4.45 % SZS status Unsatisfiable for theBenchmark.p
% 24.52/4.45
% 24.52/4.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.52/4.45
% 24.52/4.45
%------------------------------------------------------------------------------