%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 01:23:33 PM UTC 2026
% Result : Theorem 1.77s 1.50s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 22 unt; 3 def)
% Number of atoms : 121 ( 26 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 108 ( 41 ~; 33 |; 24 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 70 !; 6 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,axiom,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f36,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f45,plain,
( ~ complete
| ! [X0,X1,X2] :
( ~ shortest_path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f46,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ( path(X0,X1,sK5(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f63]) ).
fof(f66,plain,
( complete
& shortest_path(sK9,sK10,sK8)
& ~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f46]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f119,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ complete
| ~ shortest_path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f121,plain,
complete,
inference(cnf_transformation,[],[f66]) ).
fof(f122,plain,
shortest_path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f66]) ).
fof(f123,plain,
~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( minus(length_of(X2),n1) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ complete
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_103,negated_conjecture,
~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_104,negated_conjecture,
shortest_path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f122]) ).
tcf(c_105,negated_conjecture,
complete,
inference(cnf_transformation,[],[f121]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ shortest_path(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_102,c_105,c_102]) ).
tcf(c_2458,definition,
iPr_def_10 = length_of(sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2459,definition,
iPr_def_11 = minus(iPr_def_10,n1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2460,definition,
iPr_def_12 = number_of_in(triangles,graph),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2461,negated_conjecture,
shortest_path(sK9,sK10,sK8),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_2462,negated_conjecture,
~ less_or_equal(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_103,c_2460,c_2458,c_2459]) ).
tcf(c_3414,plain,
! [X0: $i] : less_or_equal(number_of_in(triangles,X0),iPr_def_12),
inference(superposition,[status(thm)],[c_2460,c_101]) ).
tcf(c_3421,plain,
path(sK9,sK10,sK8),
inference(superposition,[status(thm)],[c_2461,c_89]) ).
tcf(c_3795,plain,
number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8),
inference(superposition,[status(thm)],[c_2461,c_142]) ).
tcf(c_3826,plain,
minus(length_of(sK8),n1) = number_of_in(sequential_pairs,sK8),
inference(superposition,[status(thm)],[c_3421,c_96]) ).
tcf(c_3829,plain,
number_of_in(sequential_pairs,sK8) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3826,c_2458,c_2459]) ).
tcf(c_3864,plain,
number_of_in(triangles,sK8) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3795,c_3829]) ).
tcf(c_3865,plain,
less_or_equal(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_3864,c_3414]) ).
tcf(c_3867,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3865,c_2462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 12:45:20 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 0.22/0.50
% 0.22/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.50
% 0.22/0.50 % Detected problem language: tptp
% 0.22/0.52 % Proving...
% 1.77/1.50 % SZS status Started for theBenchmark.p
% 1.77/1.50 % SZS status Theorem for theBenchmark.p
% 1.77/1.50
% 1.77/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.77/1.50
% 1.77/1.50 % ------ iProver source info
% 1.77/1.50
% 1.77/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 1.77/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.77/1.50 % git: non_committed_changes: false
% 1.77/1.50
% 1.77/1.50 % ------ Parsing...
% 1.77/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.77/1.50
% 1.77/1.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.77/1.50
% 1.77/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.77/1.50
% 1.77/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.77/1.50 % ------ Proving...
% 1.77/1.50 % ------ Problem Properties
% 1.77/1.50
% 1.77/1.50 %
% 1.77/1.50 % clauses 58
% 1.77/1.50 % conjectures 2
% 1.77/1.50 % EPR 17
% 1.77/1.50 % Horn 40
% 1.77/1.50 % unary 8
% 1.77/1.50 % binary 15
% 1.77/1.50 % lits 173
% 1.77/1.50 % lits eq 48
% 1.77/1.50 % fd_pure 0
% 1.77/1.50 % fd_pseudo 0
% 1.77/1.50 % fd_cond 0
% 1.77/1.50 % fd_pseudo_cond 5
% 1.77/1.50 % AC symbols 0
% 1.77/1.50
% 1.77/1.50 % ------ Schedule dynamic 5 is on
% 1.77/1.50
% 1.77/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.77/1.50
% 1.77/1.50
% 1.77/1.50 % ------
% 1.77/1.50 % Current options:
% 1.77/1.50 % ------
% 1.77/1.50
% 1.77/1.50
% 1.77/1.50 %
% 1.77/1.50
% 1.77/1.50 % ------ Proving...
% 1.77/1.50 %
% 1.77/1.50
% 1.77/1.50 % SZS status Theorem for theBenchmark.p
% 1.77/1.50
% 1.77/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.77/1.50
% 1.77/1.50
%------------------------------------------------------------------------------