%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA010+1 : 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 : n009.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 01:23:38 PM UTC 2026
% Result : Theorem 3.52s 1.31s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 145 ( 34 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 160 ( 62 ~; 63 |; 27 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 78 !; 15 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
( complete
& ? [X0,X1,X2] :
( ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0)
& number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
( complete
& ? [X0,X1,X2] :
( ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0)
& number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0) ) ),
inference(flattening,[],[f43]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( sequential(sK6(X0),sK7(X0))
& on_path(sK7(X0),X0)
& on_path(sK6(X0),X0)
& ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0)),skolemize(X4,sK7(X0))],[f42]) ).
fof(f63,plain,
( complete
& ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8)
| triangle(X3,X4,sK11(X3,X4)) )
& path(sK9,sK10,sK8)
& number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X5,sK11(X3,X4))],[f44]) ).
fof(f115,plain,
! [X2,X0,X1] :
( sequential(sK6(X0),sK7(X0))
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f116,plain,
! [X2,X0,X1] :
( on_path(sK7(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f117,plain,
! [X2,X0,X1] :
( on_path(sK6(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f118,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK6(X0),sK7(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f121,plain,
! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8)
| triangle(X3,X4,sK11(X3,X4)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f122,plain,
path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f63]) ).
fof(f123,plain,
number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
inference(cnf_transformation,[],[f63]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ path(X2,X3,X0)
| ~ triangle(sK6(X0),sK7(X0),X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK6(X2),X2)
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK7(X2),X2)
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(sK6(X2),sK7(X2))
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_105,negated_conjecture,
number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
inference(cnf_transformation,[],[f123]) ).
tcf(c_106,negated_conjecture,
path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f122]) ).
tcf(c_107,negated_conjecture,
! [X0: $i,X1: $i] :
( triangle(X0,X1,sK11(X0,X1))
| ~ on_path(X1,sK8)
| ~ on_path(X0,sK8)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ on_path(X2,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X1,X2)
| ~ path(X4,X5,X0)
| ( sK7(X0) != X2 )
| ( sK6(X0) != X1 )
| ( sK11(X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_107]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ on_path(sK7(X0),sK8)
| ~ on_path(sK6(X0),sK8)
| ~ path(X1,X2,X0)
| ~ sequential(sK6(X0),sK7(X0)) ),
inference(unflattening,[status(thm)],[c_1241]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ on_path(sK7(X2),sK8)
| ~ on_path(sK6(X2),sK8)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1242,c_103]) ).
tcf(c_2232,definition,
iPr_def_10 = number_of_in(sequential_pairs,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2233,definition,
iPr_def_11 = number_of_in(triangles,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2234,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ on_path(sK7(X2),sK8)
| ~ on_path(sK6(X2),sK8)
| ~ path(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_1254]) ).
tcf(c_2238,negated_conjecture,
path(sK9,sK10,sK8),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_2239,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_105,c_2233,c_2232]) ).
tcf(c_3207,plain,
( ( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) )
| ~ on_path(sK7(sK8),sK8)
| ~ on_path(sK6(sK8),sK8) ),
inference(superposition,[status(thm)],[c_2238,c_2234]) ).
tcf(c_3208,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ on_path(sK7(sK8),sK8)
| ~ on_path(sK6(sK8),sK8) ),
inference(light_normalisation,[status(thm)],[c_3207,c_2232,c_2233]) ).
tcf(c_3209,plain,
( ~ on_path(sK7(sK8),sK8)
| ~ on_path(sK6(sK8),sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3208,c_2239]) ).
tcf(c_3896,plain,
( on_path(sK6(sK8),sK8)
| ( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) ) ),
inference(superposition,[status(thm)],[c_2238,c_101]) ).
tcf(c_3898,plain,
( on_path(sK6(sK8),sK8)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_3896,c_2232,c_2233]) ).
tcf(c_3899,plain,
on_path(sK6(sK8),sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_3898,c_2239]) ).
tcf(c_3914,plain,
( on_path(sK7(sK8),sK8)
| ( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) )
| ~ path(sK9,sK10,sK8) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_3915,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3914,c_3899,c_3209,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 12:44:29 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.52/1.31 % SZS status Started for theBenchmark.p
% 3.52/1.31 % SZS status Theorem for theBenchmark.p
% 3.52/1.31
% 3.52/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.52/1.31
% 3.52/1.31 % ------ iProver source info
% 3.52/1.31
% 3.52/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.52/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.52/1.31 % git: non_committed_changes: false
% 3.52/1.31
% 3.52/1.31 % ------ Parsing...
% 3.52/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.52/1.31
% 3.52/1.31 % ------ 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 %
% 3.52/1.31
% 3.52/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.52/1.31
% 3.52/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.52/1.31 % ------ Proving...
% 3.52/1.31 % ------ Problem Properties
% 3.52/1.31
% 3.52/1.31 %
% 3.52/1.31 % clauses 57
% 3.52/1.31 % conjectures 2
% 3.52/1.31 % EPR 15
% 3.52/1.31 % Horn 39
% 3.52/1.31 % unary 6
% 3.52/1.31 % binary 13
% 3.52/1.31 % lits 180
% 3.52/1.31 % lits eq 48
% 3.52/1.31 % fd_pure 0
% 3.52/1.31 % fd_pseudo 0
% 3.52/1.31 % fd_cond 0
% 3.52/1.31 % fd_pseudo_cond 5
% 3.52/1.31 % AC symbols 0
% 3.52/1.31
% 3.52/1.31 % ------ Schedule dynamic 5 is on
% 3.52/1.31
% 3.52/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.52/1.31
% 3.52/1.31
% 3.52/1.31 % ------
% 3.52/1.31 % Current options:
% 3.52/1.31 % ------
% 3.52/1.31
% 3.52/1.31
% 3.52/1.31 %
% 3.52/1.31
% 3.52/1.31 % ------ Proving...
% 3.52/1.31 %
% 3.52/1.31
% 3.52/1.31 % SZS status Theorem for theBenchmark.p
% 3.52/1.31
% 3.52/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.52/1.31
% 3.52/1.31
%------------------------------------------------------------------------------