%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 3.23s 1.19s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 70 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 42 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f55,axiom,
! [X0,X1] : between(X0,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
fof(f57,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
fof(f61,axiom,
! [X2,X3,X0,X1] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
fof(f85,axiom,
! [X2,X3,X0,X1,X4,X5] :
( between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
fof(f92,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f93,axiom,
equidistant(u,v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
fof(f94,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_w) ).
tcf(c_134,plain,
between(u,v,w),
inference(cnf_transformation,[],[f92]) ).
tcf(c_135,plain,
equidistant(u,v,u,w),
inference(cnf_transformation,[],[f93]) ).
tcf(c_136,negated_conjecture,
v != w,
inference(cnf_transformation,[],[f94]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( between(X5,X2,X3)
| ~ between(X4,X0,X1)
| ~ equidistant(X4,X1,X5,X3)
| ~ equidistant(X4,X0,X5,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] : between(X0,X0,X1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_744,plain,
! [X0: $i] :
( ( v = w )
| ~ between(X0,w,v)
| ~ between(X0,v,w) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_817,plain,
( ( v = w )
| ~ between(w,w,v)
| ~ between(w,v,w) ),
inference(instantiation,[status(thm)],[c_744]) ).
tcf(c_818,plain,
between(w,w,v),
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_1236,plain,
equidistant(v,w,w,v),
inference(instantiation,[status(thm)],[c_179]) ).
tcf(c_1702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(X2,w,v)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X3,w,v)
| ~ equidistant(X0,X3,X2,v)
| ~ equidistant(X0,X1,X2,w) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_1962,plain,
! [X0: $i,X1: $i] :
( between(w,X1,w)
| ~ between(X0,w,X1)
| ~ between(X0,X1,w) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_3338,plain,
! [X0: $i,X1: $i] :
( between(X1,w,v)
| ~ between(X0,v,w)
| ~ equidistant(v,w,w,v)
| ~ equidistant(X0,w,X1,v)
| ~ equidistant(X0,v,X1,w) ),
inference(instantiation,[status(thm)],[c_1702]) ).
tcf(c_4388,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X2,X0,v)
| ~ equidistant(X0,v,X1,X2) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_5008,plain,
( between(w,v,w)
| ~ between(u,w,v)
| ~ between(u,v,w) ),
inference(instantiation,[status(thm)],[c_1962]) ).
tcf(c_12582,plain,
( equidistant(u,w,u,v)
| ~ equidistant(u,v,u,w) ),
inference(instantiation,[status(thm)],[c_4388]) ).
tcf(c_19193,plain,
( between(u,w,v)
| ~ between(u,v,w)
| ~ equidistant(v,w,w,v)
| ~ equidistant(u,w,u,v)
| ~ equidistant(u,v,u,w) ),
inference(instantiation,[status(thm)],[c_3338]) ).
tcf(c_19194,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19193,c_12582,c_5008,c_1236,c_818,c_817,c_135,c_136,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n020.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 10:37:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.23/1.19 % SZS status Started for theBenchmark.p
% 3.23/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.19
% 3.23/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.19
% 3.23/1.19 % ------ iProver source info
% 3.23/1.19
% 3.23/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.19 % git: non_committed_changes: false
% 3.23/1.19
% 3.23/1.19 % ------ Parsing...% successful
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 3.23/1.19 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.19 % ------ Proving...
% 3.23/1.19 % ------ Problem Properties
% 3.23/1.19
% 3.23/1.19 %
% 3.23/1.19 % clauses 44
% 3.23/1.19 % conjectures 1
% 3.23/1.19 % EPR 44
% 3.23/1.19 % Horn 33
% 3.23/1.19 % unary 8
% 3.23/1.19 % binary 11
% 3.23/1.19 % lits 144
% 3.23/1.19 % lits eq 17
% 3.23/1.19 % fd_pure 0
% 3.23/1.19 % fd_pseudo 0
% 3.23/1.19 % fd_cond 0
% 3.23/1.19 % fd_pseudo_cond 14
% 3.23/1.19 % AC symbols 0
% 3.23/1.19
% 3.23/1.19 % ------ Schedule EPR non Horn eq is on
% 3.23/1.19
% 3.23/1.19 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 % ------
% 3.23/1.19 % Current options:
% 3.23/1.19 % ------
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % ------ Proving...
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.19
% 3.23/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.19
% 3.23/1.19
%------------------------------------------------------------------------------