%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:19:55 PM UTC 2026
% Result : Theorem 3.21s 1.18s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 149 ( 10 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 188 ( 70 ~; 64 |; 48 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 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 : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 112 ( 0 sgn 100 !; 12 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',between_o_defn) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X0] :
( incident_o(X0,X3)
<=> incident_c(X0,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o3) ).
fof(f28,conjecture,
! [X0,X1] : ~ ordered_by(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_4) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] : ~ ordered_by(X0,X1,X1),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f57,plain,
? [X0,X1] : ordered_by(X0,X1,X1),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( ? [X5] :
( inner_point(X2,X5)
& end_point(X3,X5)
& end_point(X1,X5)
& part_of(X5,X0) )
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ( ~ between_c(X0,X1,X2,X3)
| ( inner_point(X2,sK13(X0,X1,X2,X3))
& end_point(X3,sK13(X0,X1,X2,X3))
& end_point(X1,sK13(X0,X1,X2,X3))
& part_of(sK13(X0,X1,X2,X3),X0)
& X1 != X3 ) )
& ( ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3
| between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X5,sK13(X0,X1,X2,X3))],[f88]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X0,X1,X2,X3)
| ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) )
& ( ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) )
| between_o(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X0,X1,X2,X3)
| ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) )
& ( ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) )
| between_o(X0,X1,X2,X3) ) ),
inference(flattening,[],[f90]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( ( ~ incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_c(X5,X4)
| incident_o(X5,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ? [X5] :
( ( incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_o(X5,X3)
| ~ incident_c(X5,X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ? [X6] :
( between_c(X6,X0,X1,X2)
& ! [X7] :
( ( ~ incident_o(X7,X3)
| incident_c(X7,X6) )
& ( ~ incident_c(X7,X6)
| incident_o(X7,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ? [X5] :
( ( incident_o(X5,X3)
| incident_c(X5,X4) )
& ( ~ incident_o(X5,X3)
| ~ incident_c(X5,X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ( ~ between_o(X3,X0,X1,X2)
| ( between_c(sK16(X0,X1,X2,X3),X0,X1,X2)
& ! [X7] :
( ( ~ incident_o(X7,X3)
| incident_c(X7,sK16(X0,X1,X2,X3)) )
& ( ~ incident_c(X7,sK16(X0,X1,X2,X3))
| incident_o(X7,X3) ) ) ) )
& ( ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ( ( incident_o(sK15(X3,X4),X3)
| incident_c(sK15(X3,X4),X4) )
& ( ~ incident_o(sK15(X3,X4),X3)
| ~ incident_c(sK15(X3,X4),X4) ) ) )
| between_o(X3,X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X5,sK15(X3,X4)),skolemize(X6,sK16(X0,X1,X2,X3))],[f95]) ).
fof(f105,plain,
ordered_by(sK22,sK23,sK23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X0,sK22),skolemize(X1,sK23)],[f57]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f89]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f91]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ between_o(X3,X0,X1,X2)
| between_c(sK16(X0,X1,X2,X3),X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f182,plain,
ordered_by(sK22,sK23,sK23),
inference(cnf_transformation,[],[f105]) ).
fof(f187,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f152]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] : ~ between_c(X0,X1,X2,X1),
inference(cnf_transformation,[],[f187]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between_c(sK16(X1,X2,X3,X0),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_125,negated_conjecture,
ordered_by(sK22,sK23,sK23),
inference(cnf_transformation,[],[f182]) ).
tcf(c_7101,negated_conjecture,
ordered_by(sK22,sK23,sK23),
inference(demodulation,[status(thm)],[c_125]) ).
tcf(c_10638,plain,
! [X0: $i,X1: $i,X2: $i] : ~ between_o(X0,X1,X2,X1),
inference(superposition,[status(thm)],[c_114,c_92]) ).
tcf(c_10721,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_97,c_10638]) ).
tcf(c_10776,plain,
~ ordered_by(sK22,sK23,sK23),
inference(superposition,[status(thm)],[c_7101,c_10721]) ).
tcf(c_10777,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10776,c_7101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 10:57:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.21/1.18 % SZS status Started for theBenchmark.p
% 3.21/1.18 % SZS status Theorem for theBenchmark.p
% 3.21/1.18
% 3.21/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.21/1.18
% 3.21/1.18 % ------ iProver source info
% 3.21/1.18
% 3.21/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.21/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.21/1.18 % git: non_committed_changes: false
% 3.21/1.18
% 3.21/1.18 % ------ Parsing...
% 3.21/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.21/1.18
% 3.21/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.21/1.18
% 3.21/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.21/1.18
% 3.21/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.21/1.18 % ------ Proving...
% 3.21/1.18 % ------ Problem Properties
% 3.21/1.18
% 3.21/1.18 %
% 3.21/1.18 % clauses 76
% 3.21/1.18 % conjectures 1
% 3.21/1.18 % EPR 25
% 3.21/1.18 % Horn 48
% 3.21/1.18 % unary 5
% 3.21/1.18 % binary 28
% 3.21/1.18 % lits 227
% 3.21/1.18 % lits eq 21
% 3.21/1.18 % fd_pure 0
% 3.21/1.18 % fd_pseudo 0
% 3.21/1.18 % fd_cond 0
% 3.21/1.18 % fd_pseudo_cond 16
% 3.21/1.18 % AC symbols 0
% 3.21/1.18
% 3.21/1.18 % ------ Schedule dynamic 5 is on
% 3.21/1.18
% 3.21/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.21/1.18
% 3.21/1.18
% 3.21/1.18 % ------
% 3.21/1.18 % Current options:
% 3.21/1.18 % ------
% 3.21/1.18
% 3.21/1.18
% 3.21/1.18 %
% 3.21/1.18
% 3.21/1.18 % ------ Proving...
% 3.21/1.18 %
% 3.21/1.18
% 3.21/1.18 % SZS status Theorem for theBenchmark.p
% 3.21/1.18
% 3.21/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.21/1.18
%------------------------------------------------------------------------------