%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:19:30 PM UTC 2026
% Result : Unsatisfiable 3.52s 1.11s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 25 unt; 0 def)
% Number of atoms : 156 ( 68 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 139 ( 60 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
fof(f19,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
fof(f21,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
fof(f22,axiom,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f23,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_90,plain,
a != c,
inference(cnf_transformation,[],[f19]) ).
tcf(c_92,plain,
c != d,
inference(cnf_transformation,[],[f21]) ).
tcf(c_93,plain,
between(a,c,d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_94,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_95,plain,
equidistant(a,a,a,a),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_99,plain,
( ( a = a )
| ~ equidistant(a,a,a,a) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_335,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_336,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i] : extension(X0,X1,X2,X2) = X1,
inference(superposition,[status(thm)],[c_76,c_74]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] : between(X0,X1,X1),
inference(superposition,[status(thm)],[c_656,c_75]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inner_pasch(X0,X1,X2,X3,X1) = X1 )
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_79,c_78]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inner_pasch(X0,X1,X2,X0,X3) = X0 )
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_80,c_78]) ).
tcf(c_1074,plain,
! [X0: $i] :
( ( a = c )
| ( c != X0 )
| ( a != X0 ) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_1075,plain,
( ( a = c )
| ( c != a )
| ( a != a ) ),
inference(instantiation,[status(thm)],[c_1074]) ).
tcf(c_1078,plain,
! [X0: $i] :
( ( c = d )
| ( d != X0 )
| ( c != X0 ) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_1249,plain,
! [X0: $i] :
( ( c = X0 )
| ~ between(c,X0,c) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_1250,plain,
( ( c = a )
| ~ between(c,a,c) ),
inference(instantiation,[status(thm)],[c_1249]) ).
tcf(c_1427,plain,
! [X0: $i] :
( ( d = X0 )
| ~ between(d,X0,d) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_1551,plain,
( ( c = d )
| ( d != c )
| ( c != c ) ),
inference(instantiation,[status(thm)],[c_1078]) ).
tcf(c_1552,plain,
c = c,
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_1820,plain,
! [X0: $i] :
( ( inner_pasch(a,c,d,X0,c) = c )
| ~ between(c,X0,d) ),
inference(superposition,[status(thm)],[c_93,c_818]) ).
tcf(c_1821,plain,
! [X0: $i] :
( between(a,d,c)
| ( inner_pasch(c,a,d,X0,a) = a )
| ~ between(a,X0,d) ),
inference(superposition,[status(thm)],[c_335,c_818]) ).
tcf(c_1875,plain,
( between(a,d,c)
| ( inner_pasch(a,c,d,a,c) = c ) ),
inference(superposition,[status(thm)],[c_335,c_1820]) ).
tcf(c_1878,plain,
inner_pasch(a,c,d,d,c) = c,
inference(superposition,[status(thm)],[c_658,c_1820]) ).
tcf(c_1911,plain,
! [X0: $i] :
( ( inner_pasch(a,c,d,a,c) = c )
| ( inner_pasch(a,d,c,X0,d) = d )
| ~ between(d,X0,c) ),
inference(superposition,[status(thm)],[c_1875,c_818]) ).
tcf(c_1929,plain,
( between(a,d,c)
| ( inner_pasch(c,a,d,c,a) = a ) ),
inference(superposition,[status(thm)],[c_93,c_1821]) ).
tcf(c_1964,plain,
( between(d,c,a)
| ~ between(c,d,d)
| ~ between(a,c,d) ),
inference(superposition,[status(thm)],[c_1878,c_80]) ).
tcf(c_1966,plain,
between(d,c,a),
inference(forward_subsumption_resolution,[status(thm)],[c_1964,c_658,c_93]) ).
tcf(c_1967,plain,
! [X0: $i] :
( ( inner_pasch(d,c,a,X0,c) = c )
| ~ between(c,X0,a) ),
inference(superposition,[status(thm)],[c_1966,c_818]) ).
tcf(c_1975,plain,
! [X0: $i] :
( ( inner_pasch(c,a,d,c,a) = a )
| ( inner_pasch(a,d,c,X0,d) = d )
| ~ between(d,X0,c) ),
inference(superposition,[status(thm)],[c_1929,c_818]) ).
tcf(c_1997,plain,
( ( inner_pasch(a,d,c,c,d) = d )
| ( inner_pasch(a,c,d,a,c) = c ) ),
inference(superposition,[status(thm)],[c_658,c_1911]) ).
tcf(c_2202,plain,
( between(c,d,a)
| ( inner_pasch(a,c,d,a,c) = c )
| ~ between(d,c,c)
| ~ between(a,d,c) ),
inference(superposition,[status(thm)],[c_1997,c_80]) ).
tcf(c_2204,plain,
( between(c,d,a)
| ( inner_pasch(a,c,d,a,c) = c )
| ~ between(a,d,c) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2202,c_658]) ).
tcf(c_2225,plain,
( ( inner_pasch(c,a,d,c,a) = a )
| ( inner_pasch(a,d,c,c,d) = d ) ),
inference(superposition,[status(thm)],[c_658,c_1975]) ).
tcf(c_2320,plain,
( between(c,a,c)
| ( inner_pasch(a,d,c,c,d) = d )
| ~ between(c,a,d)
| ~ between(a,c,d) ),
inference(superposition,[status(thm)],[c_2225,c_80]) ).
tcf(c_2322,plain,
( between(c,a,c)
| ( inner_pasch(a,d,c,c,d) = d )
| ~ between(c,a,d) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2320,c_93]) ).
tcf(c_2336,plain,
( between(c,d,a)
| ( inner_pasch(a,c,d,a,c) = c ) ),
inference(global_subsumption_just,[status(thm)],[c_2204,c_1875,c_2204]) ).
tcf(c_2351,plain,
( ~ between(c,a,d)
| ( inner_pasch(a,d,c,c,d) = d ) ),
inference(global_subsumption_just,[status(thm)],[c_2322,c_90,c_95,c_99,c_1075,c_1250,c_2322]) ).
tcf(c_2352,plain,
( ( inner_pasch(a,d,c,c,d) = d )
| ~ between(c,a,d) ),
inference(renaming,[status(thm)],[c_2351]) ).
tcf(c_2357,plain,
( between(a,d,c)
| ( inner_pasch(a,d,c,c,d) = d ) ),
inference(superposition,[status(thm)],[c_335,c_2352]) ).
tcf(c_2364,plain,
! [X0: $i] :
( ( inner_pasch(a,d,c,c,d) = d )
| ( inner_pasch(a,d,c,X0,d) = d )
| ~ between(d,X0,c) ),
inference(superposition,[status(thm)],[c_2357,c_818]) ).
tcf(c_2383,plain,
! [X0: $i] :
( ( inner_pasch(a,c,d,a,X0) = a )
| ~ between(X0,a,d) ),
inference(superposition,[status(thm)],[c_93,c_835]) ).
tcf(c_2701,plain,
inner_pasch(a,d,c,c,d) = d,
inference(superposition,[status(thm)],[c_658,c_2364]) ).
tcf(c_2740,plain,
( between(a,d,c)
| ( inner_pasch(a,c,d,a,c) = a ) ),
inference(superposition,[status(thm)],[c_335,c_2383]) ).
tcf(c_2892,plain,
( between(c,d,a)
| ~ between(d,c,c)
| ~ between(a,d,c) ),
inference(superposition,[status(thm)],[c_2701,c_80]) ).
tcf(c_2894,plain,
( between(c,d,a)
| ~ between(a,d,c) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2892,c_658]) ).
tcf(c_2903,plain,
( between(c,d,a)
| ( inner_pasch(a,c,d,a,c) = a ) ),
inference(superposition,[status(thm)],[c_2740,c_2894]) ).
tcf(c_3389,plain,
( ( inner_pasch(d,c,a,d,c) = c )
| ( inner_pasch(a,c,d,a,c) = a ) ),
inference(superposition,[status(thm)],[c_2903,c_1967]) ).
tcf(c_4646,plain,
( ( d = c )
| ~ between(d,c,d) ),
inference(instantiation,[status(thm)],[c_1427]) ).
tcf(c_5307,plain,
( between(d,c,d)
| ( inner_pasch(a,c,d,a,c) = a )
| ~ between(d,c,a)
| ~ between(c,d,a) ),
inference(superposition,[status(thm)],[c_3389,c_80]) ).
tcf(c_5309,plain,
( between(d,c,d)
| ( inner_pasch(a,c,d,a,c) = a )
| ~ between(c,d,a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5307,c_1966]) ).
tcf(c_5582,plain,
inner_pasch(a,c,d,a,c) = a,
inference(global_subsumption_just,[status(thm)],[c_5309,c_92,c_1551,c_1552,c_2903,c_4646,c_5309]) ).
tcf(c_5589,plain,
( between(c,d,a)
| ( a = c ) ),
inference(demodulation,[status(thm)],[c_2336,c_5582]) ).
tcf(c_5593,plain,
between(c,d,a),
inference(forward_subsumption_resolution,[status(thm)],[c_5589,c_90]) ).
tcf(c_5615,plain,
inner_pasch(d,c,a,d,c) = c,
inference(superposition,[status(thm)],[c_5593,c_1967]) ).
tcf(c_5882,plain,
( between(d,c,d)
| ~ between(d,c,a)
| ~ between(c,d,a) ),
inference(superposition,[status(thm)],[c_5615,c_80]) ).
tcf(c_5884,plain,
between(d,c,d),
inference(forward_subsumption_resolution,[status(thm)],[c_5882,c_1966,c_5593]) ).
tcf(c_5885,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5884,c_4646,c_1552,c_1551,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:22:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.52/1.11 % SZS status Started for theBenchmark.p
% 3.52/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 3.52/1.11
% 3.52/1.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.52/1.11
% 3.52/1.11 % ------ iProver source info
% 3.52/1.11
% 3.52/1.11 % git: date: 2026-07-19 20:42:38 +0200
% 3.52/1.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.52/1.11 % git: non_committed_changes: false
% 3.52/1.11
% 3.52/1.11 % ------ Parsing...% successful
% 3.52/1.11
% 3.52/1.11
% 3.52/1.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.52/1.11
% 3.52/1.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.52/1.11
% 3.52/1.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.52/1.11
% 3.52/1.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.52/1.11 % ------ Proving...
% 3.52/1.11 % ------ Problem Properties
% 3.52/1.11
% 3.52/1.11 %
% 3.52/1.11 % clauses 23
% 3.52/1.11 % conjectures 1
% 3.52/1.11 % EPR 14
% 3.52/1.11 % Horn 17
% 3.52/1.11 % unary 10
% 3.52/1.11 % binary 3
% 3.52/1.11 % lits 62
% 3.52/1.11 % lits eq 10
% 3.52/1.11 % fd_pure 0
% 3.52/1.11 % fd_pseudo 0
% 3.52/1.11 % fd_cond 0
% 3.52/1.11 % fd_pseudo_cond 7
% 3.52/1.11 % AC symbols 0
% 3.52/1.11
% 3.52/1.11 % ------ Schedule dynamic 5 is on
% 3.52/1.11
% 3.52/1.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.52/1.11
% 3.52/1.11
% 3.52/1.11 % ------
% 3.52/1.11 % Current options:
% 3.52/1.11 % ------
% 3.52/1.11
% 3.52/1.11
% 3.52/1.11 %
% 3.52/1.11
% 3.52/1.11 % ------ Proving...
% 3.52/1.11 %
% 3.52/1.11
% 3.52/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 3.52/1.11
% 3.52/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.52/1.11
% 3.52/1.11
%------------------------------------------------------------------------------