%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO068-3 : 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 : n019.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 01:19:46 PM UTC 2026
% Result : Unsatisfiable 17.95s 18.69s
% Output : CNFRefutation 17.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 71 ~; 77 |; 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 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X2,X0,X1] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
fof(f20,axiom,
! [X2,X0,X1] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
fof(f22,axiom,
! [X2,X0,X1] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
fof(f89,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/sandbox/benchmark/theBenchmark.p',b11) ).
fof(f101,axiom,
! [X2,X0,X1] :
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_2) ).
fof(f110,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f111,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f112,axiom,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
fof(f113,axiom,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uvw_colinear) ).
fof(f114,negated_conjecture,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u1v1w1_colinear) ).
tcf(c_154,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[],[f110]) ).
tcf(c_155,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[],[f111]) ).
tcf(c_156,plain,
equidistant(u,w,u1,w1),
inference(cnf_transformation,[],[f112]) ).
tcf(c_157,plain,
colinear(u,v,w),
inference(cnf_transformation,[],[f113]) ).
tcf(c_158,negated_conjecture,
~ colinear(u1,v1,w1),
inference(cnf_transformation,[],[f114]) ).
tcf(c_160,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,[],[f89]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_905,plain,
( colinear(u1,v1,w1)
| ~ between(w1,u1,v1) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_906,plain,
( colinear(u1,v1,w1)
| ~ between(v1,w1,u1) ),
inference(instantiation,[status(thm)],[c_197]) ).
tcf(c_907,plain,
( colinear(u1,v1,w1)
| ~ between(u1,v1,w1) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_3464,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X0,w1,u1)
| ~ equidistant(X0,X1,u1,w1) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_3493,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X0,w1,v1)
| ~ equidistant(X0,X1,v1,w1) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_3522,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,X0,v1,u1)
| ~ equidistant(X0,X1,u1,v1) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_5393,plain,
( equidistant(w,u,w1,u1)
| ~ equidistant(u,w,u1,w1) ),
inference(instantiation,[status(thm)],[c_3464]) ).
tcf(c_5536,plain,
( equidistant(w,v,w1,v1)
| ~ equidistant(v,w,v1,w1) ),
inference(instantiation,[status(thm)],[c_3493]) ).
tcf(c_5671,plain,
( equidistant(v,u,v1,u1)
| ~ equidistant(u,v,u1,v1) ),
inference(instantiation,[status(thm)],[c_3522]) ).
tcf(c_17026,plain,
! [X0: $i,X1: $i,X2: $i] :
( between(w1,u1,v1)
| ~ between(X2,X0,X1)
| ~ equidistant(X2,X1,w1,v1)
| ~ equidistant(X2,X0,w1,u1)
| ~ equidistant(X0,X1,u1,v1) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_18247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(v1,w1,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X3,X0,v1,w1)
| ~ equidistant(X3,X1,v1,X2)
| ~ equidistant(X0,X1,w1,X2) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_18301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( between(u1,v1,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X3,X0,u1,v1)
| ~ equidistant(X3,X1,u1,X2)
| ~ equidistant(X0,X1,v1,X2) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_25631,plain,
! [X0: $i,X1: $i] :
( between(v1,w1,X1)
| ~ between(v,w,X0)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(w,X0,w1,X1)
| ~ equidistant(v,X0,v1,X1) ),
inference(instantiation,[status(thm)],[c_18247]) ).
tcf(c_25674,plain,
! [X0: $i,X1: $i] :
( between(u1,v1,X1)
| ~ between(u,v,X0)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1) ),
inference(instantiation,[status(thm)],[c_18301]) ).
tcf(c_26411,plain,
! [X0: $i] :
( between(w,u,X0)
| between(u,X0,w)
| between(X0,w,u)
| ~ colinear(X0,w,u) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_30862,plain,
! [X0: $i] :
( between(w1,u1,v1)
| ~ between(w,X0,v)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,X0,w1,u1)
| ~ equidistant(X0,v,u1,v1) ),
inference(instantiation,[status(thm)],[c_17026]) ).
tcf(c_40922,plain,
! [X0: $i] :
( colinear(X0,w,u)
| ~ colinear(u,X0,w) ),
inference(instantiation,[status(thm)],[c_190]) ).
tcf(c_43768,plain,
( between(v1,w1,u1)
| ~ between(v,w,u)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(v,u,v1,u1) ),
inference(instantiation,[status(thm)],[c_25631]) ).
tcf(c_43887,plain,
( between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1)
| ~ equidistant(u,v,u1,v1) ),
inference(instantiation,[status(thm)],[c_25674]) ).
tcf(c_52289,plain,
( colinear(v,w,u)
| ~ colinear(u,v,w) ),
inference(instantiation,[status(thm)],[c_40922]) ).
tcf(c_66472,plain,
( between(w,u,v)
| between(v,w,u)
| between(u,v,w)
| ~ colinear(v,w,u) ),
inference(instantiation,[status(thm)],[c_26411]) ).
tcf(c_116744,plain,
( between(w1,u1,v1)
| ~ between(w,u,v)
| ~ equidistant(w,v,w1,v1)
| ~ equidistant(w,u,w1,u1)
| ~ equidistant(u,v,u1,v1) ),
inference(instantiation,[status(thm)],[c_30862]) ).
tcf(c_116745,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116744,c_66472,c_52289,c_43887,c_43768,c_5671,c_5536,c_5393,c_907,c_906,c_905,c_154,c_155,c_156,c_158,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO068-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/15.39 % Computer : n019.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Wed Sep 23 10:41:54 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/15.43 Running first-order theorem proving
% 0.14/15.43 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
% 0.14/15.44
% 0.14/15.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/15.44
% 0.14/15.44 % Detected problem language: tptp
% 0.14/15.45 % Proving...
% 17.95/18.69 % SZS status Started for theBenchmark.p
% 17.95/18.69 % SZS status Unsatisfiable for theBenchmark.p
% 17.95/18.69
% 17.95/18.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.95/18.69
% 17.95/18.69 % ------ iProver source info
% 17.95/18.69
% 17.95/18.69 % git: date: 2026-07-19 20:42:38 +0200
% 17.95/18.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.95/18.69 % git: non_committed_changes: false
% 17.95/18.69
% 17.95/18.69 % ------ Parsing...% successful
% 17.95/18.69
% 17.95/18.69
% 17.95/18.69 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 17.95/18.69 %
% 17.95/18.69
% 17.95/18.69 % ------ 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 %
% 17.95/18.69
% 17.95/18.69 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 17.95/18.69 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 17.95/18.69 %
% 17.95/18.69
% 17.95/18.69 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.95/18.69 % ------ Proving...
% 17.95/18.69 % ------ Problem Properties
% 17.95/18.69
% 17.95/18.69 %
% 17.95/18.69 % clauses 62
% 17.95/18.69 % conjectures 1
% 17.95/18.69 % EPR 62
% 17.95/18.69 % Horn 50
% 17.95/18.69 % unary 13
% 17.95/18.69 % binary 22
% 17.95/18.69 % lits 178
% 17.95/18.69 % lits eq 17
% 17.95/18.69 % fd_pure 0
% 17.95/18.69 % fd_pseudo 0
% 17.95/18.69 % fd_cond 0
% 17.95/18.69 % fd_pseudo_cond 15
% 17.95/18.69 % AC symbols 0
% 17.95/18.69
% 17.95/18.69 % ------ Schedule EPR non Horn eq is on
% 17.95/18.69
% 17.95/18.69 % ------ Option_epr_non_horn_eq Time Limit: Unbounded
% 17.95/18.69
% 17.95/18.69
% 17.95/18.69 % ------
% 17.95/18.69 % Current options:
% 17.95/18.69 % ------
% 17.95/18.69
% 17.95/18.69
% 17.95/18.69 %
% 17.95/18.69
% 17.95/18.69 % ------ Proving...
% 17.95/18.69 %
% 17.95/18.69
% 17.95/18.69 % SZS status Unsatisfiable for theBenchmark.p
% 17.95/18.69
% 17.95/18.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.95/18.69
% 17.95/18.69
%------------------------------------------------------------------------------