%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:23:38 PM UTC 2026
% Result : Theorem 1.35s 1.18s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 11 unt; 2 def)
% Number of atoms : 139 ( 30 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 142 ( 52 ~; 55 |; 27 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 86 ( 0 sgn 71 !; 15 ?; 23 :)
% 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/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f19,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/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f20,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)],[f19]) ).
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(ennf_transformation,[],[f16]) ).
fof(f43,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,[],[f42]) ).
fof(f46,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,[],[f20]) ).
fof(f47,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,[],[f46]) ).
fof(f65,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))],[f43]) ).
fof(f67,plain,
( complete
& ! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK9)
| ~ on_path(X3,sK9)
| triangle(X3,X4,sK12(X3,X4)) )
& path(sK10,sK11,sK9)
& number_of_in(sequential_pairs,sK9) != number_of_in(triangles,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X5,sK12(X3,X4))],[f47]) ).
fof(f119,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,[],[f65]) ).
fof(f120,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,[],[f65]) ).
fof(f121,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,[],[f65]) ).
fof(f122,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,[],[f65]) ).
fof(f126,plain,
! [X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,sK9)
| ~ on_path(X3,sK9)
| triangle(X3,X4,sK12(X3,X4)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f127,plain,
path(sK10,sK11,sK9),
inference(cnf_transformation,[],[f67]) ).
fof(f128,plain,
number_of_in(sequential_pairs,sK9) != number_of_in(triangles,sK9),
inference(cnf_transformation,[],[f67]) ).
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,[],[f122]) ).
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,[],[f121]) ).
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,[],[f120]) ).
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,[],[f119]) ).
tcf(c_106,negated_conjecture,
number_of_in(sequential_pairs,sK9) != number_of_in(triangles,sK9),
inference(cnf_transformation,[],[f128]) ).
tcf(c_107,negated_conjecture,
path(sK10,sK11,sK9),
inference(cnf_transformation,[],[f127]) ).
tcf(c_108,negated_conjecture,
! [X0: $i,X1: $i] :
( triangle(X0,X1,sK12(X0,X1))
| ~ on_path(X1,sK9)
| ~ on_path(X0,sK9)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_2669,definition,
iPr_def_10 = number_of_in(sequential_pairs,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2670,definition,
iPr_def_11 = number_of_in(triangles,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2671,negated_conjecture,
! [X0: $i,X1: $i] :
( triangle(X0,X1,sK12(X0,X1))
| ~ on_path(X1,sK9)
| ~ on_path(X0,sK9)
| ~ sequential(X0,X1) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_2672,negated_conjecture,
path(sK10,sK11,sK9),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_2673,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_106,c_2670,c_2669]) ).
tcf(c_4405,plain,
( on_path(sK6(sK9),sK9)
| ( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ) ),
inference(superposition,[status(thm)],[c_2672,c_101]) ).
tcf(c_4408,plain,
( on_path(sK6(sK9),sK9)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_4405,c_2669,c_2670]) ).
tcf(c_4409,plain,
on_path(sK6(sK9),sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_4408,c_2673]) ).
tcf(c_4635,plain,
( on_path(sK7(sK9),sK9)
| ( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ) ),
inference(superposition,[status(thm)],[c_2672,c_102]) ).
tcf(c_4640,plain,
( on_path(sK7(sK9),sK9)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_4635,c_2669,c_2670]) ).
tcf(c_4641,plain,
on_path(sK7(sK9),sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_4640,c_2673]) ).
tcf(c_5212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ on_path(sK7(X0),sK9)
| ~ on_path(sK6(X0),sK9)
| ~ path(X1,X2,X0)
| ~ sequential(sK6(X0),sK7(X0)) ),
inference(superposition,[status(thm)],[c_2671,c_100]) ).
tcf(c_5456,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ on_path(sK7(X2),sK9)
| ~ on_path(sK6(X2),sK9)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5212,c_103]) ).
tcf(c_5472,plain,
( ( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) )
| ~ on_path(sK7(sK9),sK9)
| ~ on_path(sK6(sK9),sK9) ),
inference(superposition,[status(thm)],[c_2672,c_5456]) ).
tcf(c_5478,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ on_path(sK7(sK9),sK9)
| ~ on_path(sK6(sK9),sK9) ),
inference(light_normalisation,[status(thm)],[c_5472,c_2669,c_2670]) ).
tcf(c_5479,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5478,c_2673,c_4641,c_4409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.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 12:47:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.35/1.18 % SZS status Started for theBenchmark.p
% 1.35/1.18 % SZS status Theorem for theBenchmark.p
% 1.35/1.18
% 1.35/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.35/1.18
% 1.35/1.18 % ------ iProver source info
% 1.35/1.18
% 1.35/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.35/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.35/1.18 % git: non_committed_changes: false
% 1.35/1.18
% 1.35/1.18 % ------ Parsing...
% 1.35/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.35/1.18
% 1.35/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.35/1.18
% 1.35/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.35/1.18
% 1.35/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.35/1.18 % ------ Proving...
% 1.35/1.18 % ------ Problem Properties
% 1.35/1.18
% 1.35/1.18 %
% 1.35/1.18 % clauses 62
% 1.35/1.18 % conjectures 3
% 1.35/1.18 % EPR 22
% 1.35/1.18 % Horn 44
% 1.35/1.18 % unary 6
% 1.35/1.18 % binary 19
% 1.35/1.18 % lits 187
% 1.35/1.18 % lits eq 47
% 1.35/1.18 % fd_pure 0
% 1.35/1.18 % fd_pseudo 0
% 1.35/1.18 % fd_cond 0
% 1.35/1.18 % fd_pseudo_cond 5
% 1.35/1.18 % AC symbols 0
% 1.35/1.18
% 1.35/1.18 % ------ Schedule dynamic 5 is on
% 1.35/1.18
% 1.35/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.35/1.18
% 1.35/1.18
% 1.35/1.18 % ------
% 1.35/1.18 % Current options:
% 1.35/1.18 % ------
% 1.35/1.18
% 1.35/1.18
% 1.35/1.18 %
% 1.35/1.18
% 1.35/1.18 % ------ Proving...
% 1.35/1.18 %
% 1.35/1.18
% 1.35/1.18 % SZS status Theorem for theBenchmark.p
% 1.35/1.18
% 1.35/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.35/1.18
% 1.35/1.18
%------------------------------------------------------------------------------