%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 03:45:25 PM UTC 2026
% Result : Theorem 0.94s 1.06s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 84 ( 31 ~; 23 |; 18 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 63 ( 0 sgn 57 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0,X1,X2] :
( ( r(X1,X2)
& r(X0,X1) )
=> r(X0,X2) )
& ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0,X1,X2] :
( ( r(X1,X2)
& r(X0,X1) )
=> r(X0,X2) )
& ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X2,X3,X4] :
( ( r(X3,X4)
& r(X2,X3) )
=> r(X2,X4) )
& ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) ) )
=> ! [X5,X6] :
( r(X5,X6)
=> r(X5,X5) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X2,X3,X4] :
( ~ r(X3,X4)
| ~ r(X2,X3)
| r(X2,X4) )
& ! [X0,X1] :
( ~ r(X0,X1)
| r(X1,X0) )
& ? [X5,X6] :
( r(X5,X6)
& ~ r(X5,X5) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X2,X3,X4] :
( ~ r(X3,X4)
| ~ r(X2,X3)
| r(X2,X4) )
& ! [X0,X1] :
( ~ r(X0,X1)
| r(X1,X0) )
& ? [X5,X6] :
( r(X5,X6)
& ~ r(X5,X5) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X4,X5,X6] :
( ~ r(X5,X6)
| ~ r(X4,X5)
| r(X4,X6) )
& ! [X2,X3] :
( ~ r(X2,X3)
| r(X3,X2) )
& ? [X0,X1] :
( r(X0,X1)
& ~ r(X0,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X4,X5,X6] :
( ~ r(X5,X6)
| ~ r(X4,X5)
| r(X4,X6) )
& ! [X2,X3] :
( ~ r(X2,X3)
| r(X3,X2) )
& r(sK0,sK1)
& ~ r(sK0,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
fof(f8,plain,
! [X6,X4,X5] :
( ~ r(X5,X6)
| ~ r(X4,X5)
| r(X4,X6) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3] :
( ~ r(X2,X3)
| r(X3,X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
r(sK0,sK1),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
~ r(sK0,sK0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
~ r(sK0,sK0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_50,negated_conjecture,
r(sK0,sK1),
inference(cnf_transformation,[],[f10]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( r(X1,X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r(X0,X2)
| ~ r(X1,X2)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( r(X0,X2)
| ~ r(X1,X2)
| ~ r(X0,X1) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( r(X1,X0)
| ~ r(X0,X1) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_55,negated_conjecture,
r(sK0,sK1),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_57,plain,
r(sK1,sK0),
inference(resolution,[status(thm)],[c_54,c_55]) ).
tcf(c_58,plain,
! [X0: $i] :
( r(sK0,X0)
| ~ r(sK1,X0) ),
inference(resolution,[status(thm)],[c_53,c_55]) ).
tcf(c_59,plain,
( r(sK0,sK0)
| ~ r(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_60,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59,c_57,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Fri Sep 25 02:34:06 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 0.94/1.06 % SZS status Started for theBenchmark.p
% 0.94/1.06 % SZS status Theorem for theBenchmark.p
% 0.94/1.06
% 0.94/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.06
% 0.94/1.06 % ------ iProver source info
% 0.94/1.06
% 0.94/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.06 % git: non_committed_changes: false
% 0.94/1.06
% 0.94/1.06 % ------ Parsing...
% 0.94/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_horn
% 0.94/1.06 %
% 0.94/1.06
% 0.94/1.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 0.94/1.06
% 0.94/1.06 % ------ Preprocessing...% ------ preprocesses with Option_epr_horn
% 0.94/1.06 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.94/1.06 % ------ Proving...
% 0.94/1.06 % ------ Problem Properties
% 0.94/1.06
% 0.94/1.06 %
% 0.94/1.06 % clauses 4
% 0.94/1.06 % conjectures 4
% 0.94/1.06 % EPR 4
% 0.94/1.06 % Horn 4
% 0.94/1.06 % unary 2
% 0.94/1.06 % binary 1
% 0.94/1.06 % lits 7
% 0.94/1.06 % lits eq 0
% 0.94/1.06 % fd_pure 0
% 0.94/1.06 % fd_pseudo 0
% 0.94/1.06 % fd_cond 0
% 0.94/1.06 % fd_pseudo_cond 0
% 0.94/1.06 % AC symbols 0
% 0.94/1.06
% 0.94/1.06 % ------ Schedule EPR Horn non eq is on
% 0.94/1.06
% 0.94/1.06 % ------ no equalities: superposition off
% 0.94/1.06
% 0.94/1.06 % ------ Option_epr_horn Time Limit: Unbounded
% 0.94/1.06
% 0.94/1.06
% 0.94/1.06 % ------
% 0.94/1.06 % Current options:
% 0.94/1.06 % ------
% 0.94/1.06
% 0.94/1.06
% 0.94/1.06 %
% 0.94/1.06
% 0.94/1.06 % ------ Proving...
% 0.94/1.06 %
% 0.94/1.06
% 0.94/1.06 % SZS status Theorem for theBenchmark.p
% 0.94/1.06
% 0.94/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.06
% 0.94/1.06
%------------------------------------------------------------------------------