%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 6.81s 1.74s
% Output : CNFRefutation 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 124 ( 22 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 155 ( 65 ~; 61 |; 26 &)
% ( 1 <=>; 2 =>; 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 117 ( 0 sgn 109 !; 8 ?; 49 :)
% 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/sandbox2/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(f18,conjecture,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> between_c(X0,X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_2) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> between_c(X0,X3,X2,X1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
& ~ between_c(X0,X3,X2,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f68,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(f69,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,[],[f68]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f72,plain,
( between_c(sK14,sK15,sK16,sK17)
& ~ between_c(sK14,sK17,sK16,sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X3,sK17)],[f41]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| inner_point(X2,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X3,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X1,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| part_of(sK13(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f71]) ).
fof(f119,plain,
! [X2,X3,X0,X1,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(cnf_transformation,[],[f71]) ).
fof(f120,plain,
between_c(sK14,sK15,sK16,sK17),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
~ between_c(sK14,sK17,sK16,sK15),
inference(cnf_transformation,[],[f72]) ).
fof(f126,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f118]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between_c(X1,X2,X4,X3)
| ( X2 = X3 )
| ~ inner_point(X4,X0)
| ~ end_point(X3,X0)
| ~ end_point(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : ~ between_c(X0,X1,X2,X1),
inference(cnf_transformation,[],[f126]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( part_of(sK13(X0,X1,X2,X3),X0)
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( end_point(X1,sK13(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( end_point(X3,sK13(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( inner_point(X2,sK13(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_96,negated_conjecture,
~ between_c(sK14,sK17,sK16,sK15),
inference(cnf_transformation,[],[f121]) ).
tcf(c_97,negated_conjecture,
between_c(sK14,sK15,sK16,sK17),
inference(cnf_transformation,[],[f120]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 != sK16 )
| ( X1 != sK15 )
| ( X1 != sK17 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_97]) ).
tcf(c_568,plain,
sK17 != sK15,
inference(unflattening,[status(thm)],[c_567]) ).
tcf(c_2503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( between_c(X4,X5,X2,X6)
| ( X5 = X6 )
| ~ between_c(X0,X1,X2,X3)
| ~ end_point(X6,sK13(X0,X1,X2,X3))
| ~ end_point(X5,sK13(X0,X1,X2,X3))
| ~ part_of(sK13(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[c_90,c_95]) ).
tcf(c_2533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( between_c(X4,X5,X2,X1)
| ( X5 = X1 )
| ~ between_c(X0,X1,X2,X3)
| ~ end_point(X5,sK13(X0,X1,X2,X3))
| ~ part_of(sK13(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[c_2503,c_93]) ).
tcf(c_2563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between_c(X4,X3,X2,X1)
| ( X3 = X1 )
| ~ between_c(X0,X1,X2,X3)
| ~ part_of(sK13(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[c_2533,c_94]) ).
tcf(c_2618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between_c(X0,X3,X2,X1)
| ( X3 = X1 )
| ~ between_c(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c_2563,c_92]) ).
tcf(c_2625,plain,
( between_c(sK14,sK17,sK16,sK15)
| ( sK17 = sK15 ) ),
inference(resolution,[status(thm)],[c_2618,c_97]) ).
tcf(c_2626,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2625,c_568,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n010.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 10:56:43 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...
% 6.81/1.74 % SZS status Started for theBenchmark.p
% 6.81/1.74 % SZS status Theorem for theBenchmark.p
% 6.81/1.74
% 6.81/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.81/1.74
% 6.81/1.74 % ------ iProver source info
% 6.81/1.74
% 6.81/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 6.81/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.81/1.74 % git: non_committed_changes: false
% 6.81/1.74
% 6.81/1.74 % ------ Parsing...
% 6.81/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.81/1.74
% 6.81/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.81/1.74
% 6.81/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.81/1.74
% 6.81/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.81/1.74 % ------ Proving...
% 6.81/1.74 % ------ Problem Properties
% 6.81/1.74
% 6.81/1.74 %
% 6.81/1.74 % clauses 49
% 6.81/1.74 % conjectures 2
% 6.81/1.74 % EPR 17
% 6.81/1.74 % Horn 32
% 6.81/1.74 % unary 4
% 6.81/1.74 % binary 20
% 6.81/1.74 % lits 146
% 6.81/1.74 % lits eq 13
% 6.81/1.74 % fd_pure 0
% 6.81/1.74 % fd_pseudo 0
% 6.81/1.74 % fd_cond 0
% 6.81/1.74 % fd_pseudo_cond 8
% 6.81/1.74 % AC symbols 0
% 6.81/1.74
% 6.81/1.74 % ------ Input Options Time Limit: Unbounded
% 6.81/1.74
% 6.81/1.74
% 6.81/1.74 % ------
% 6.81/1.74 % Current options:
% 6.81/1.74 % ------
% 6.81/1.74
% 6.81/1.74
% 6.81/1.74 %
% 6.81/1.74
% 6.81/1.74 % ------ Proving...
% 6.81/1.74 %
% 6.81/1.74
% 6.81/1.74 % SZS status Theorem for theBenchmark.p
% 6.81/1.74
% 6.81/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.81/1.74
% 6.81/1.74
%------------------------------------------------------------------------------