%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO048-2 : 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 : n015.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 01:19:41 PM UTC 2026
% Result : Unsatisfiable 1.27s 6.29s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 23 unt; 2 def)
% Number of atoms : 76 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 32 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-5 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
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(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,
between(u1,v1,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
fof(f21,axiom,
between(u,x,u1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_between_u_and_u1) ).
fof(f23,negated_conjecture,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_conclusion2) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,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_80,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_90,plain,
between(u,v,w),
inference(cnf_transformation,[],[f19]) ).
tcf(c_91,plain,
between(u1,v1,w),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,plain,
between(u,x,u1),
inference(cnf_transformation,[],[f21]) ).
tcf(c_94,negated_conjecture,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(cnf_transformation,[],[f23]) ).
tcf(c_330,definition,
iPr_def_10 = inner_pasch(u,x,u1,v1,w),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_331,definition,
iPr_def_11 = inner_pasch(v1,iPr_def_10,u,v,w),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_332,negated_conjecture,
~ between(v,iPr_def_11,v1),
inference(demodulation,[status(thm)],[c_94,c_330,c_331]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_76,c_74]) ).
tcf(c_682,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_680,c_75]) ).
tcf(c_809,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_79,c_78]) ).
tcf(c_826,plain,
( between(v1,iPr_def_10,u)
| ~ between(w,v1,u1)
| ~ between(u,x,u1) ),
inference(superposition,[status(thm)],[c_330,c_80]) ).
tcf(c_827,plain,
( between(v,iPr_def_11,v1)
| ~ between(v1,iPr_def_10,u)
| ~ between(w,v,u) ),
inference(superposition,[status(thm)],[c_331,c_80]) ).
tcf(c_829,plain,
( ~ between(v1,iPr_def_10,u)
| ~ between(w,v,u) ),
inference(forward_subsumption_resolution,[status(thm)],[c_827,c_332]) ).
tcf(c_832,plain,
( between(v1,iPr_def_10,u)
| ~ between(w,v1,u1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_826,c_92]) ).
tcf(c_2424,plain,
! [X0: $i] :
( ( inner_pasch(u,v,w,X0,v) = v )
| ~ between(v,X0,w) ),
inference(superposition,[status(thm)],[c_90,c_809]) ).
tcf(c_2425,plain,
! [X0: $i] :
( ( inner_pasch(u1,v1,w,X0,v1) = v1 )
| ~ between(v1,X0,w) ),
inference(superposition,[status(thm)],[c_91,c_809]) ).
tcf(c_2523,plain,
inner_pasch(u,v,w,w,v) = v,
inference(superposition,[status(thm)],[c_682,c_2424]) ).
tcf(c_2543,plain,
inner_pasch(u1,v1,w,w,v1) = v1,
inference(superposition,[status(thm)],[c_682,c_2425]) ).
tcf(c_2606,plain,
( between(w,v,u)
| ~ between(v,w,w)
| ~ between(u,v,w) ),
inference(superposition,[status(thm)],[c_2523,c_80]) ).
tcf(c_2608,plain,
between(w,v,u),
inference(forward_subsumption_resolution,[status(thm)],[c_2606,c_682,c_90]) ).
tcf(c_2609,plain,
~ between(v1,iPr_def_10,u),
inference(backward_subsumption_resolution,[status(thm)],[c_829,c_2608]) ).
tcf(c_2610,plain,
~ between(w,v1,u1),
inference(backward_subsumption_resolution,[status(thm)],[c_832,c_2609]) ).
tcf(c_2615,plain,
( between(w,v1,u1)
| ~ between(v1,w,w)
| ~ between(u1,v1,w) ),
inference(superposition,[status(thm)],[c_2543,c_80]) ).
tcf(c_2617,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2615,c_2610,c_682,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 10:38:03 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.27/6.29 % SZS status Started for theBenchmark.p
% 1.27/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/6.29
% 1.27/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.27/6.29
% 1.27/6.29 % ------ iProver source info
% 1.27/6.29
% 1.27/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.27/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.27/6.29 % git: non_committed_changes: false
% 1.27/6.29
% 1.27/6.29 % ------ Parsing...% successful
% 1.27/6.29
% 1.27/6.29
% 1.27/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.27/6.29
% 1.27/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.27/6.29
% 1.27/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.27/6.29
% 1.27/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.27/6.29 % ------ Proving...
% 1.27/6.29 % ------ Problem Properties
% 1.27/6.29
% 1.27/6.29 %
% 1.27/6.29 % clauses 25
% 1.27/6.29 % conjectures 2
% 1.27/6.29 % EPR 14
% 1.27/6.29 % Horn 20
% 1.27/6.29 % unary 13
% 1.27/6.29 % binary 2
% 1.27/6.29 % lits 63
% 1.27/6.29 % lits eq 9
% 1.27/6.29 % fd_pure 0
% 1.27/6.29 % fd_pseudo 0
% 1.27/6.29 % fd_cond 0
% 1.27/6.29 % fd_pseudo_cond 7
% 1.27/6.29 % AC symbols 0
% 1.27/6.29
% 1.27/6.29 % ------ Schedule dynamic 5 is on
% 1.27/6.29
% 1.27/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.27/6.29
% 1.27/6.29
% 1.27/6.29 % ------
% 1.27/6.29 % Current options:
% 1.27/6.29 % ------
% 1.27/6.29
% 1.27/6.29
% 1.27/6.29 %
% 1.27/6.29
% 1.27/6.29 % ------ Proving...
% 1.27/6.29 %
% 1.27/6.29
% 1.27/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/6.29
% 1.27/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.27/6.30
% 1.27/6.30
%------------------------------------------------------------------------------