%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:19:36 PM UTC 2026
% Result : Unsatisfiable 0.91s 6.22s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 23 unt; 2 def)
% Number of atoms : 81 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
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(f31,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| X0 != extension(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4] :
( between(X1,X2,X0)
| extension(X1,X2,X3,X4) != X0 ),
inference(reorient_equations,[],[f31]) ).
fof(f43,axiom,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
fof(f44,axiom,
equidistant(w,x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
fof(f45,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f46,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_extensions) ).
fof(f52,plain,
! [X2,X3,X1,X4] : between(X1,X2,extension(X1,X2,X3,X4)),
inference(equality_resolution,[],[f32]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_109,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_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X3 )
| ~ between(X3,X0,X2)
| ~ between(X3,X0,X1)
| ~ equidistant(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_127,plain,
equidistant(w,x,y,z),
inference(cnf_transformation,[],[f44]) ).
tcf(c_128,plain,
u != v,
inference(cnf_transformation,[],[f45]) ).
tcf(c_129,negated_conjecture,
extension(u,v,w,x) != extension(u,v,y,z),
inference(cnf_transformation,[],[f46]) ).
tcf(c_829,definition,
iPr_def_10 = extension(u,v,w,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_830,definition,
iPr_def_11 = extension(u,v,y,z),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_831,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_129,c_830,c_829]) ).
tcf(c_1296,plain,
between(u,v,iPr_def_10),
inference(superposition,[status(thm)],[c_829,c_118]) ).
tcf(c_1298,plain,
between(u,v,iPr_def_11),
inference(superposition,[status(thm)],[c_830,c_118]) ).
tcf(c_1300,plain,
equidistant(v,iPr_def_10,w,x),
inference(superposition,[status(thm)],[c_829,c_94]) ).
tcf(c_1301,plain,
equidistant(v,iPr_def_11,y,z),
inference(superposition,[status(thm)],[c_830,c_94]) ).
tcf(c_1319,plain,
equidistant(y,z,w,x),
inference(superposition,[status(thm)],[c_127,c_109]) ).
tcf(c_1322,plain,
equidistant(w,x,v,iPr_def_10),
inference(superposition,[status(thm)],[c_1300,c_109]) ).
tcf(c_1323,plain,
equidistant(y,z,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1301,c_109]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i] :
( equidistant(w,x,X0,X1)
| ~ equidistant(y,z,X0,X1) ),
inference(superposition,[status(thm)],[c_1319,c_91]) ).
tcf(c_1528,plain,
! [X0: $i,X1: $i] :
( equidistant(v,iPr_def_10,X0,X1)
| ~ equidistant(w,x,X0,X1) ),
inference(superposition,[status(thm)],[c_1322,c_91]) ).
tcf(c_5543,plain,
equidistant(w,x,v,iPr_def_11),
inference(superposition,[status(thm)],[c_1323,c_1526]) ).
tcf(c_7397,plain,
equidistant(v,iPr_def_10,v,iPr_def_11),
inference(superposition,[status(thm)],[c_5543,c_1528]) ).
tcf(c_7577,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_11 )
| ( X0 = v )
| ~ between(X0,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7397,c_126]) ).
tcf(c_7583,plain,
! [X0: $i] :
( ( X0 = v )
| ~ between(X0,v,iPr_def_11)
| ~ between(X0,v,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7577,c_831]) ).
tcf(c_7748,plain,
( ( u = v )
| ~ between(u,v,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1296,c_7583]) ).
tcf(c_7749,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7748,c_128,c_1298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO028-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 10:30:44 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 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
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 0.91/6.22 % SZS status Started for theBenchmark.p
% 0.91/6.22 % SZS status Unsatisfiable for theBenchmark.p
% 0.91/6.22
% 0.91/6.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.91/6.22
% 0.91/6.22 % ------ iProver source info
% 0.91/6.22
% 0.91/6.22 % git: date: 2026-07-19 20:42:38 +0200
% 0.91/6.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.91/6.22 % git: non_committed_changes: false
% 0.91/6.22
% 0.91/6.22 % ------ Parsing...% successful
% 0.91/6.22
% 0.91/6.22
% 0.91/6.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.91/6.22
% 0.91/6.22 % ------ Preprocessing... sup_sim: 0 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 %
% 0.91/6.22
% 0.91/6.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.91/6.22
% 0.91/6.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.91/6.22 % ------ Proving...
% 0.91/6.22 % ------ Problem Properties
% 0.91/6.22
% 0.91/6.22 %
% 0.91/6.22 % clauses 37
% 0.91/6.22 % conjectures 1
% 0.91/6.22 % EPR 24
% 0.91/6.22 % Horn 31
% 0.91/6.22 % unary 14
% 0.91/6.22 % binary 10
% 0.91/6.22 % lits 93
% 0.91/6.22 % lits eq 16
% 0.91/6.22 % fd_pure 0
% 0.91/6.22 % fd_pseudo 0
% 0.91/6.22 % fd_cond 0
% 0.91/6.22 % fd_pseudo_cond 9
% 0.91/6.22 % AC symbols 0
% 0.91/6.22
% 0.91/6.22 % ------ Schedule dynamic 5 is on
% 0.91/6.22
% 0.91/6.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.91/6.22
% 0.91/6.22
% 0.91/6.22 % ------
% 0.91/6.22 % Current options:
% 0.91/6.22 % ------
% 0.91/6.22
% 0.91/6.22
% 0.91/6.22 %
% 0.91/6.22
% 0.91/6.22 % ------ Proving...
% 0.91/6.22 %
% 0.91/6.22
% 0.91/6.22 % SZS status Unsatisfiable for theBenchmark.p
% 0.91/6.22
% 0.91/6.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.91/6.22
% 0.91/6.22
%------------------------------------------------------------------------------