%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA005+1 : 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 : n014.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 01:23:34 PM UTC 2026
% Result : Theorem 0.27s 1.07s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 20 unt; 4 def)
% Number of atoms : 95 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 37 ~; 21 |; 23 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 69 ( 0 sgn 54 !; 15 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2)
& edge(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_short_cut_edge) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2)
& edge(X5) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2)
& edge(X5) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2)
& edge(X5) ) ),
inference(flattening,[],[f43]) ).
fof(f61,plain,
( precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11)
& head_of(sK10) = head_of(sK12)
& tail_of(sK9) = tail_of(sK12)
& edge(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f44]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
head_of(sK10) = head_of(sK12),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
tail_of(sK9) = tail_of(sK12),
inference(cnf_transformation,[],[f61]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X0,X3)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_97,negated_conjecture,
tail_of(sK12) = tail_of(sK9),
inference(cnf_transformation,[],[f112]) ).
tcf(c_98,negated_conjecture,
head_of(sK12) = head_of(sK10),
inference(cnf_transformation,[],[f111]) ).
tcf(c_99,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f110]) ).
tcf(c_100,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f109]) ).
tcf(c_1919,definition,
iPr_def_10 = head_of(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1920,definition,
iPr_def_11 = head_of(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1921,definition,
iPr_def_12 = tail_of(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1922,definition,
iPr_def_13 = tail_of(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1923,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1924,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1925,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_98,c_1920,c_1919]) ).
tcf(c_1926,negated_conjecture,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_97,c_1922,c_1921]) ).
tcf(c_2691,plain,
head_of(sK10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1920,c_1925]) ).
tcf(c_2692,plain,
tail_of(sK9) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1922,c_1926]) ).
tcf(c_4495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X1,sK10,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2691,c_86]) ).
tcf(c_5532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(sK9,sK10,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != iPr_def_12 )
| ( head_of(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2692,c_4495]) ).
tcf(c_5628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ precedes(sK9,sK10,X2)
| ~ shortest_path(X0,X1,X2)
| ( tail_of(sK12) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1919,c_5532]) ).
tcf(c_5629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ precedes(sK9,sK10,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(ground_joinability,[status(thm)],[c_5628,c_1921]) ).
tcf(c_5645,plain,
~ precedes(sK9,sK10,sK11),
inference(superposition,[status(thm)],[c_1924,c_5629]) ).
tcf(c_5646,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5645,c_1923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:43:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 0.27/1.07 % SZS status Started for theBenchmark.p
% 0.27/1.07 % SZS status Theorem for theBenchmark.p
% 0.27/1.07
% 0.27/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.27/1.07
% 0.27/1.07 % ------ iProver source info
% 0.27/1.07
% 0.27/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.27/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.27/1.07 % git: non_committed_changes: false
% 0.27/1.07
% 0.27/1.07 % ------ Parsing...
% 0.27/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.27/1.07
% 0.27/1.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.27/1.07
% 0.27/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.27/1.07
% 0.27/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.27/1.07 % ------ Proving...
% 0.27/1.07 % ------ Problem Properties
% 0.27/1.07
% 0.27/1.07 %
% 0.27/1.07 % clauses 50
% 0.27/1.07 % conjectures 5
% 0.27/1.07 % EPR 17
% 0.27/1.07 % Horn 37
% 0.27/1.07 % unary 12
% 0.27/1.07 % binary 10
% 0.27/1.07 % lits 133
% 0.27/1.07 % lits eq 32
% 0.27/1.07 % fd_pure 0
% 0.27/1.07 % fd_pseudo 0
% 0.27/1.07 % fd_cond 0
% 0.27/1.07 % fd_pseudo_cond 3
% 0.27/1.07 % AC symbols 0
% 0.27/1.07
% 0.27/1.07 % ------ Schedule dynamic 5 is on
% 0.27/1.07
% 0.27/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.27/1.07
% 0.27/1.07
% 0.27/1.07 % ------
% 0.27/1.07 % Current options:
% 0.27/1.07 % ------
% 0.27/1.07
% 0.27/1.07
% 0.27/1.07 %
% 0.27/1.07
% 0.27/1.07 % ------ Proving...
% 0.27/1.07 %
% 0.27/1.07
% 0.27/1.07 % SZS status Theorem for theBenchmark.p
% 0.27/1.07
% 0.27/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.27/1.07
% 0.27/1.07
%------------------------------------------------------------------------------