%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:57:22 PM UTC 2026
% Result : Theorem 2.28s 1.28s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 20 unt; 2 def)
% Number of atoms : 176 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 195 ( 82 ~; 63 |; 48 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 51 !; 7 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3] :
~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X1,X3)
& r2_hidden(X0,X3) )
& ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
& r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = k2_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
| r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,X3) )
& ( ~ r2_hidden(X1,k4_xboole_0(X2,X3))
| ~ r2_hidden(X0,k4_xboole_0(X2,X3)) )
& r2_hidden(X1,k2_xboole_0(X2,X3))
& r2_hidden(X0,k2_xboole_0(X2,X3)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
( ( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,sK3) )
& ( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) )
& ( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) )
& ( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) )
& r2_hidden(sK1,k2_xboole_0(sK2,sK3))
& r2_hidden(sK0,k2_xboole_0(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f27]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X0) )
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X0) )
| r2_hidden(X4,X2) ) ) )
& ( ( ( r2_hidden(sK4(X0,X1,X2),X2)
| r2_hidden(sK4(X0,X1,X2),X1)
| r2_hidden(sK4(X0,X1,X2),X0) )
& ( ~ r2_hidden(sK4(X0,X1,X2),X2)
| ( ~ r2_hidden(sK4(X0,X1,X2),X1)
& ~ r2_hidden(sK4(X0,X1,X2),X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f40]) ).
fof(f45,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f46,plain,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f47,plain,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f48,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
r2_hidden(sK1,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f53,plain,
! [X2,X0,X1,X4] :
( k2_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
fof(f77,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k2_xboole_0(X0,X1))
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f53]) ).
tcf(c_49,negated_conjecture,
r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_50,negated_conjecture,
r2_hidden(sK1,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_51,negated_conjecture,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_52,negated_conjecture,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_53,negated_conjecture,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_54,negated_conjecture,
( ~ r2_hidden(sK0,sK3)
| ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X2)
| r2_hidden(X0,X1)
| ~ r2_hidden(X0,k2_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
inference(cnf_transformation,[],[f69]) ).
tcf(c_222,plain,
r2_hidden(sK0,k2_xboole_0(sK3,sK2)),
inference(demodulation,[status(thm)],[c_49,c_56]) ).
tcf(c_223,plain,
r2_hidden(sK1,k2_xboole_0(sK3,sK2)),
inference(demodulation,[status(thm)],[c_50,c_56]) ).
tcf(c_498,definition,
iPr_def_10 = k2_xboole_0(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_499,definition,
iPr_def_11 = k4_xboole_0(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_500,plain,
r2_hidden(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_223,c_498]) ).
tcf(c_501,plain,
r2_hidden(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_222]) ).
tcf(c_502,negated_conjecture,
( ~ r2_hidden(sK1,iPr_def_11)
| ~ r2_hidden(sK0,sK3) ),
inference(demodulation,[status(thm)],[c_54,c_499]) ).
tcf(c_503,negated_conjecture,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_505,negated_conjecture,
( ~ r2_hidden(sK1,iPr_def_11)
| ~ r2_hidden(sK0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_872,plain,
k2_xboole_0(sK3,sK2) = k2_xboole_0(sK3,iPr_def_11),
inference(superposition,[status(thm)],[c_499,c_73]) ).
tcf(c_877,plain,
k2_xboole_0(sK3,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_872,c_498]) ).
tcf(c_943,plain,
k2_xboole_0(iPr_def_11,sK3) = iPr_def_10,
inference(demodulation,[status(thm)],[c_877,c_56]) ).
tcf(c_1047,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_11)
| r2_hidden(X0,sK3)
| ~ r2_hidden(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_943,c_62]) ).
tcf(c_1889,plain,
( r2_hidden(sK1,iPr_def_11)
| r2_hidden(sK1,sK3) ),
inference(superposition,[status(thm)],[c_500,c_1047]) ).
tcf(c_1890,plain,
( r2_hidden(sK0,iPr_def_11)
| r2_hidden(sK0,sK3) ),
inference(superposition,[status(thm)],[c_501,c_1047]) ).
tcf(c_1949,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1889,c_1890,c_505,c_503,c_502,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 13:56:47 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 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
% 0.24/0.50
% 0.24/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.50
% 0.24/0.50 % Detected problem language: tptp
% 0.24/0.51 % Proving...
% 2.28/1.28 % SZS status Started for theBenchmark.p
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.28
% 2.28/1.28 % ------ iProver source info
% 2.28/1.28
% 2.28/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.28 % git: non_committed_changes: false
% 2.28/1.28
% 2.28/1.28 % ------ Parsing...
% 2.28/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 % ------ Problem Properties
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28 % clauses 30
% 2.28/1.28 % conjectures 4
% 2.28/1.28 % EPR 13
% 2.28/1.28 % Horn 27
% 2.28/1.28 % unary 13
% 2.28/1.28 % binary 12
% 2.28/1.28 % lits 53
% 2.28/1.28 % lits eq 13
% 2.28/1.28 % fd_pure 0
% 2.28/1.28 % fd_pseudo 0
% 2.28/1.28 % fd_cond 1
% 2.28/1.28 % fd_pseudo_cond 4
% 2.28/1.28 % AC symbols 0
% 2.28/1.28
% 2.28/1.28 % ------ Schedule dynamic 5 is on
% 2.28/1.28
% 2.28/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 % ------
% 2.28/1.28 % Current options:
% 2.28/1.28 % ------
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.28
% 2.28/1.28
%------------------------------------------------------------------------------