%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:19:37 PM UTC 2026
% Result : Unsatisfiable 6.90s 1.70s
% Output : CNFRefutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 119 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 142 ( 72 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f20,axiom,
! [X0,X1] : equidistant(X0,X1,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
fof(f51,axiom,
! [X0,X1] : between(X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f54,axiom,
! [X0,X1] : between(X0,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
fof(f75,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X1,X2,X4,X5)
| ~ equidistant(X0,X2,X3,X5)
| ~ equidistant(X0,X1,X3,X4)
| ~ between(X3,X4,X5)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13) ).
fof(f76,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14) ).
fof(f77,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f78,axiom,
equidistant(u,v,u,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u_to_x) ).
fof(f79,axiom,
equidistant(w,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_v_equals_w_to_x) ).
fof(f80,negated_conjecture,
v != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_is_x) ).
tcf(c_121,plain,
between(u,v,w),
inference(cnf_transformation,[],[f77]) ).
tcf(c_122,plain,
equidistant(u,v,u,x),
inference(cnf_transformation,[],[f78]) ).
tcf(c_123,plain,
equidistant(w,v,w,x),
inference(cnf_transformation,[],[f79]) ).
tcf(c_124,negated_conjecture,
v != x,
inference(cnf_transformation,[],[f80]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X0,X6,X2,X7)
| ~ between(X5,X2,X3)
| ~ between(X4,X0,X1)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X4,X0,X5,X2)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X1,X4,X3,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : between(X0,X0,X1),
inference(cnf_transformation,[],[f54]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(cnf_transformation,[],[f51]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_889,plain,
equidistant(x,v,v,x),
inference(instantiation,[status(thm)],[c_159]) ).
tcf(c_1007,plain,
between(v,v,x),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_1015,plain,
between(v,x,x),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_1302,plain,
! [X0: $i] :
( ( v = x )
| ~ equidistant(v,x,X0,X0) ),
inference(instantiation,[status(thm)],[c_157]) ).
tcf(c_1317,plain,
! [X0: $i] :
( equidistant(v,x,X0,X0)
| ~ equidistant(X0,X0,v,x) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_1328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equidistant(v,x,X2,X2)
| ~ between(X3,v,X0)
| ~ between(X4,X2,X1)
| ~ equidistant(v,X0,X2,X1)
| ~ equidistant(X3,x,X4,X2)
| ~ equidistant(X3,v,X4,X2)
| ~ equidistant(X0,x,X1,X2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_1523,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X0,v,x)
| ~ equidistant(X0,X1,v,x) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_1654,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,x,X0,X1)
| ~ equidistant(X0,X1,X2,x) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_1702,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(v,x,X1,X1)
| ~ between(u,v,w)
| ~ between(X0,X1,X2)
| ~ equidistant(w,x,X2,X1)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,x,X0,X1)
| ~ equidistant(u,v,X0,X1) ),
inference(instantiation,[status(thm)],[c_1328]) ).
tcf(c_2286,plain,
( equidistant(v,x,v,x)
| ~ equidistant(x,v,v,x) ),
inference(instantiation,[status(thm)],[c_1523]) ).
tcf(c_2610,plain,
( equidistant(u,x,u,v)
| ~ equidistant(u,v,u,x) ),
inference(instantiation,[status(thm)],[c_1654]) ).
tcf(c_2611,plain,
( equidistant(w,x,w,v)
| ~ equidistant(w,v,w,x) ),
inference(instantiation,[status(thm)],[c_1654]) ).
tcf(c_3644,plain,
! [X0: $i] : equidistant(X0,v,X0,v),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_4549,plain,
! [X0: $i] :
( equidistant(v,x,v,v)
| ~ between(u,v,w)
| ~ between(X0,v,w)
| ~ equidistant(w,x,w,v)
| ~ equidistant(v,w,v,w)
| ~ equidistant(u,x,X0,v)
| ~ equidistant(u,v,X0,v) ),
inference(instantiation,[status(thm)],[c_1702]) ).
tcf(c_4550,plain,
equidistant(v,w,v,w),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_5635,plain,
equidistant(u,v,u,v),
inference(instantiation,[status(thm)],[c_3644]) ).
tcf(c_8939,plain,
( equidistant(v,x,x,x)
| ~ equidistant(x,x,v,x) ),
inference(instantiation,[status(thm)],[c_1317]) ).
tcf(c_11299,plain,
( ( v = x )
| ~ equidistant(v,x,x,x) ),
inference(instantiation,[status(thm)],[c_1302]) ).
tcf(c_14661,plain,
( equidistant(v,x,v,v)
| ~ between(u,v,w)
| ~ equidistant(w,x,w,v)
| ~ equidistant(v,w,v,w)
| ~ equidistant(u,x,u,v)
| ~ equidistant(u,v,u,v) ),
inference(instantiation,[status(thm)],[c_4549]) ).
tcf(c_21785,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X1,X1,v,x)
| ~ between(X2,v,x)
| ~ between(X0,X1,X1)
| ~ equidistant(X0,X1,X2,x)
| ~ equidistant(X0,X1,X2,v) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_23776,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X1,v,x)
| ~ between(v,v,x)
| ~ between(X0,X1,X1)
| ~ equidistant(X0,X1,v,x)
| ~ equidistant(X0,X1,v,v) ),
inference(instantiation,[status(thm)],[c_21785]) ).
tcf(c_28235,plain,
( equidistant(x,x,v,x)
| ~ between(v,x,x)
| ~ between(v,v,x)
| ~ equidistant(v,x,v,x)
| ~ equidistant(v,x,v,v) ),
inference(instantiation,[status(thm)],[c_23776]) ).
tcf(c_28236,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28235,c_14661,c_11299,c_8939,c_5635,c_4550,c_2611,c_2610,c_2286,c_1015,c_1007,c_889,c_122,c_123,c_124,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 10:30:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 6.90/1.70 % SZS status Started for theBenchmark.p
% 6.90/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.90/1.70
% 6.90/1.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.90/1.70
% 6.90/1.70 % ------ iProver source info
% 6.90/1.70
% 6.90/1.70 % git: date: 2026-07-19 20:42:38 +0200
% 6.90/1.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.90/1.70 % git: non_committed_changes: false
% 6.90/1.70
% 6.90/1.70 % ------ Parsing...% successful
% 6.90/1.70
% 6.90/1.70
% 6.90/1.70 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 6.90/1.70 %
% 6.90/1.70
% 6.90/1.70 % ------ 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 %
% 6.90/1.70
% 6.90/1.70 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 6.90/1.70 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 6.90/1.70 %
% 6.90/1.70
% 6.90/1.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.90/1.70 % ------ Proving...
% 6.90/1.70 % ------ Problem Properties
% 6.90/1.70
% 6.90/1.70 %
% 6.90/1.70 % clauses 37
% 6.90/1.70 % conjectures 1
% 6.90/1.70 % EPR 37
% 6.90/1.70 % Horn 31
% 6.90/1.70 % unary 9
% 6.90/1.70 % binary 11
% 6.90/1.70 % lits 109
% 6.90/1.70 % lits eq 13
% 6.90/1.70 % fd_pure 0
% 6.90/1.70 % fd_pseudo 0
% 6.90/1.70 % fd_cond 0
% 6.90/1.70 % fd_pseudo_cond 10
% 6.90/1.70 % AC symbols 0
% 6.90/1.70
% 6.90/1.70 % ------ Schedule EPR non Horn eq is on
% 6.90/1.70
% 6.90/1.70 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 6.90/1.70
% 6.90/1.70
% 6.90/1.70 % ------
% 6.90/1.70 % Current options:
% 6.90/1.70 % ------
% 6.90/1.70
% 6.90/1.70
% 6.90/1.70 %
% 6.90/1.70
% 6.90/1.70 % ------ Proving...
% 6.90/1.70 %
% 6.90/1.70
% 6.90/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.90/1.70
% 6.90/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.90/1.70
% 6.90/1.70
%------------------------------------------------------------------------------