%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:03:16 PM UTC 2026
% Result : Unsatisfiable 3.67s 0.81s
% Output : Proof 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 38 unt; 0 def)
% Number of atoms : 70 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',direct_success) ).
fof(f0_nnf,plain,
! [Goal_state,Start_state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Goal_state,Start_state] :
( ~ follows(Goal_state,Start_state)
| succeeds(Goal_state,Start_state) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ follows(X0,X1)
| succeeds(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(follows(X0,X1),true,succeeds(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f12,hypothesis,
follows(p6,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_3_to_6) ).
fof(f12_nnf,plain,
follows(p6,p3),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
follows(p6,p3),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
follows(p6,p3) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h4,plain,
succeeds(p6,p3) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi12]) ).
cnf(f14,hypothesis,
follows(p7,p6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_6_to_7) ).
fof(f14_nnf,plain,
follows(p7,p6),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
follows(p7,p6),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,axiom,
follows(p7,p6) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h5,plain,
succeeds(p7,p6) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi14]) ).
cnf(f1,axiom,
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_success) ).
fof(f1_nnf,plain,
! [Goal_state,Start_state,Intermediate_state] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Goal_state,Start_state,Intermediate_state] :
( ~ succeeds(Intermediate_state,Start_state)
| ~ succeeds(Goal_state,Intermediate_state)
| succeeds(Goal_state,Start_state) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ succeeds(X2,X1)
| ~ succeeds(X0,X2)
| succeeds(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(succeeds(X0,X1),true,ifeq(succeeds(X1,X2),true,succeeds(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h12,plain,
succeeds(p7,p3) = true,
inference(hyper_resolution,[status(thm)],[hi1,h5,h4]) ).
cnf(f16,hypothesis,
follows(p8,p7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_7_to_8) ).
fof(f16_nnf,plain,
follows(p8,p7),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
follows(p8,p7),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
follows(p8,p7) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h6,plain,
succeeds(p8,p7) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi16]) ).
cnf(f2,axiom,
( ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label))
| succeeds(Goal_state,Start_state) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goto_success) ).
fof(f2_nnf,plain,
! [Goal_state,Start_state,Label] :
( ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label))
| succeeds(Goal_state,Start_state) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Goal_state,Start_state,Label] :
( ~ labels(Label,Goal_state)
| ~ has(Start_state,goto(Label))
| succeeds(Goal_state,Start_state) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ labels(X2,X0)
| ~ has(X1,goto(X2))
| succeeds(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(has(X0,goto(X1)),true,ifeq(labels(X1,X2),true,succeeds(X2,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f17,hypothesis,
has(p8,goto(loop)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_8) ).
fof(f17_nnf,plain,
has(p8,goto(loop)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
has(p8,goto(loop)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
has(p8,goto(loop)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f7,hypothesis,
labels(loop,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',label_state_3) ).
fof(f7_nnf,plain,
labels(loop,p3),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
labels(loop,p3),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
labels(loop,p3) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h7,plain,
succeeds(p3,p8) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi17,hi7]) ).
cnf(h16,plain,
succeeds(p3,p7) = true,
inference(hyper_resolution,[status(thm)],[hi1,h7,h6]) ).
cnf(t10,plain,
succeeds(p3,p3) = true,
inference(hyper_resolution,[status(thm)],[hi1,h16,h12]) ).
cnf(t57,plain,
succeeds(p3,p3) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f18,negated_conjecture,
~ succeeds(p3,p3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
fof(f18_nnf,plain,
~ succeeds(p3,p3),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ succeeds(p3,p3),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ succeeds(p3,p3),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
succeeds(p3,p3) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t57]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Fri Sep 25 07:42:35 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.67/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.67/0.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------