%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO030-3 : 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 : n005.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 20.71s 4.67s
% Output : CNFRefutation 20.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 109 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 134 ( 65 ~; 69 |; 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 : 85 ( 0 sgn 85 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
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(f25,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
fof(f27,axiom,
! [X2,X3,X0,X1] :
( equidistant(X3,X2,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
fof(f42,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X4,X2,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
fof(f73,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f74,axiom,
equidistant(u,w,u,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u_to_w1) ).
fof(f75,axiom,
equidistant(v,w,v,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_w1) ).
fof(f76,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f77,negated_conjecture,
w != w1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_w1) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( equidistant(X1,X4,X3,X5)
| ( X0 = X6 )
| ~ between(X7,X2,X3)
| ~ between(X6,X0,X1)
| ~ equidistant(X6,X4,X7,X5)
| ~ equidistant(X6,X0,X7,X2)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_137,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_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(X3,X2,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X4,X1,X5,X3)
| ~ between(X5,X2,X3)
| ~ between(X4,X0,X1)
| ~ equidistant(X4,X0,X5,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_180,plain,
between(u,v,w),
inference(cnf_transformation,[],[f73]) ).
tcf(c_181,plain,
equidistant(u,w,u,w1),
inference(cnf_transformation,[],[f74]) ).
tcf(c_182,plain,
equidistant(v,w,v,w1),
inference(cnf_transformation,[],[f75]) ).
tcf(c_183,plain,
u != v,
inference(cnf_transformation,[],[f76]) ).
tcf(c_184,negated_conjecture,
w != w1,
inference(cnf_transformation,[],[f77]) ).
tcf(c_509,plain,
equidistant(w1,v,w,v),
inference(superposition,[status(thm)],[c_182,c_143]) ).
tcf(c_562,plain,
equidistant(u,w1,u,w),
inference(superposition,[status(thm)],[c_181,c_137]) ).
tcf(c_563,plain,
equidistant(v,w1,v,w),
inference(superposition,[status(thm)],[c_182,c_137]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i] :
( equidistant(X0,w,X1,w1)
| ~ between(X1,v,w1)
| ~ between(X0,v,w)
| ~ equidistant(X0,v,X1,v) ),
inference(superposition,[status(thm)],[c_182,c_153]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equidistant(X5,X1,X5,X2)
| ( X0 = X3 )
| ~ between(X4,X0,X5)
| ~ between(X3,X0,X5)
| ~ equidistant(X3,X1,X4,X2)
| ~ equidistant(X3,X0,X4,X0)
| ~ equidistant(X0,X1,X0,X2) ),
inference(superposition,[status(thm)],[c_136,c_123]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equidistant(v,X1,v,X3)
| ( X0 = w1 )
| ~ between(X2,w,v)
| ~ between(X0,w1,v)
| ~ equidistant(w1,X1,w,X3)
| ~ equidistant(X0,w1,X2,w)
| ~ equidistant(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_509,c_123]) ).
tcf(c_1311,plain,
! [X0: $i] :
( equidistant(X0,w,X0,w1)
| ~ between(X0,v,w1)
| ~ between(X0,v,w) ),
inference(superposition,[status(thm)],[c_136,c_690]) ).
tcf(c_1573,plain,
! [X0: $i,X1: $i,X2: $i] :
( equidistant(X2,w1,X2,w)
| ( X0 = v )
| ~ between(X1,v,X2)
| ~ between(X0,v,X2)
| ~ equidistant(X0,w1,X1,w)
| ~ equidistant(X0,v,X1,v) ),
inference(superposition,[status(thm)],[c_563,c_764]) ).
tcf(c_3335,plain,
! [X0: $i] :
( equidistant(X0,w1,w,X0)
| ~ between(X0,v,w1)
| ~ between(X0,v,w) ),
inference(superposition,[status(thm)],[c_1311,c_141]) ).
tcf(c_4456,plain,
! [X0: $i,X1: $i] :
( equidistant(X1,w1,X1,w)
| ( X0 = v )
| ~ between(X0,v,X1)
| ~ equidistant(X0,w1,X0,w) ),
inference(superposition,[status(thm)],[c_136,c_1573]) ).
tcf(c_7840,plain,
! [X0: $i] :
( equidistant(v,w1,v,X0)
| ( X0 = w1 )
| ~ between(w,w,v)
| ~ between(X0,w1,v)
| ~ between(X0,v,w1)
| ~ between(X0,v,w)
| ~ equidistant(w1,w1,w,X0)
| ~ equidistant(X0,w1,w,w) ),
inference(superposition,[status(thm)],[c_3335,c_806]) ).
tcf(c_15561,plain,
! [X0: $i] :
( equidistant(X0,w1,X0,w)
| ( u = v )
| ~ between(u,v,X0) ),
inference(superposition,[status(thm)],[c_562,c_4456]) ).
tcf(c_18455,plain,
! [X0: $i] :
( ( X0 = w1 )
| ~ equidistant(X0,w1,w,w) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7840,c_120,c_120,c_120,c_120,c_120,c_120]) ).
tcf(c_39856,plain,
! [X0: $i] :
( equidistant(X0,w1,X0,w)
| ~ between(u,v,X0) ),
inference(global_subsumption_just,[status(thm)],[c_15561,c_183,c_15561]) ).
tcf(c_40005,plain,
( ( w = w1 )
| ~ between(u,v,w) ),
inference(superposition,[status(thm)],[c_39856,c_18455]) ).
tcf(c_40038,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_40005,c_184,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO030-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 10:28:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 20.71/4.67 % SZS status Started for theBenchmark.p
% 20.71/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 20.71/4.67
% 20.71/4.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.71/4.67
% 20.71/4.67 % ------ iProver source info
% 20.71/4.67
% 20.71/4.67 % git: date: 2026-07-19 20:42:38 +0200
% 20.71/4.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.71/4.67 % git: non_committed_changes: false
% 20.71/4.67
% 20.71/4.67 % ------ Parsing...% successful
% 20.71/4.67
% 20.71/4.67
% 20.71/4.67 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.71/4.67 % ------ Proving...
% 20.71/4.67 % ------ Problem Properties
% 20.71/4.67
% 20.71/4.67 %
% 20.71/4.67 % clauses 67
% 20.71/4.67 % conjectures 1
% 20.71/4.67 % EPR 42
% 20.71/4.67 % Horn 53
% 20.71/4.67 % unary 29
% 20.71/4.67 % binary 13
% 20.71/4.67 % lits 156
% 20.71/4.67 % lits eq 35
% 20.71/4.67 % fd_pure 0
% 20.71/4.67 % fd_pseudo 0
% 20.71/4.67 % fd_cond 0
% 20.71/4.67 % fd_pseudo_cond 17
% 20.71/4.67 % AC symbols 0
% 20.71/4.67
% 20.71/4.67 % ------ Input Options Time Limit: Unbounded
% 20.71/4.67
% 20.71/4.67
% 20.71/4.67 % ------
% 20.71/4.67 % Current options:
% 20.71/4.67 % ------
% 20.71/4.67
% 20.71/4.67
% 20.71/4.67 %
% 20.71/4.67
% 20.71/4.67 % ------ Proving...
% 20.71/4.67 %
% 20.71/4.67
% 20.71/4.67 % ------ Proving...
% 20.71/4.67 %
% 20.71/4.67
% 20.71/4.67 % ------ Proving...
% 20.71/4.67 %
% 20.71/4.67
% 20.71/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 20.71/4.67
% 20.71/4.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.71/4.67
% 20.71/4.67
%------------------------------------------------------------------------------