TSTP Solution File: SEU126+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:03:52 EDT 2023
% Result : Theorem 2.41s 1.16s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 152 ( 27 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 183 ( 67 ~; 70 |; 36 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn; 57 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
inference(negated_conjecture,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,plain,
? [X0,X1] :
( set_union2(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK0(X0,X1,X2),X1)
& ~ in(sK0(X0,X1,X2),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f35,f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f39,f40]) ).
fof(f46,plain,
( ? [X0,X1] :
( set_union2(X0,X1) != X1
& subset(X0,X1) )
=> ( sK5 != set_union2(sK4,sK5)
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
( sK5 != set_union2(sK4,sK5)
& subset(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f46]) ).
fof(f49,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f56,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f47]) ).
fof(f70,plain,
sK5 != set_union2(sK4,sK5),
inference(cnf_transformation,[],[f47]) ).
cnf(c_50,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f49]) ).
cnf(c_55,plain,
( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_56,plain,
( set_union2(X0,X1) = X2
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_62,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_70,negated_conjecture,
set_union2(sK4,sK5) != sK5,
inference(cnf_transformation,[],[f70]) ).
cnf(c_71,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f69]) ).
cnf(c_200,plain,
set_union2(sK5,sK4) != sK5,
inference(demodulation,[status(thm)],[c_70,c_50]) ).
cnf(c_1205,plain,
( ~ in(sK0(sK5,sK4,sK5),sK5)
| set_union2(sK5,sK4) = sK5 ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_1206,plain,
( set_union2(sK5,sK4) = sK5
| in(sK0(sK5,sK4,sK5),sK5)
| in(sK0(sK5,sK4,sK5),sK4) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_1225,plain,
( ~ in(sK0(sK5,sK4,sK5),sK4)
| ~ subset(sK4,X0)
| in(sK0(sK5,sK4,sK5),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_2070,plain,
( ~ in(sK0(sK5,sK4,sK5),sK4)
| ~ subset(sK4,sK5)
| in(sK0(sK5,sK4,sK5),sK5) ),
inference(instantiation,[status(thm)],[c_1225]) ).
cnf(c_2071,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2070,c_1206,c_1205,c_200,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 19:21:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.41/1.16 % SZS status Started for theBenchmark.p
% 2.41/1.16 % SZS status Theorem for theBenchmark.p
% 2.41/1.16
% 2.41/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.41/1.16
% 2.41/1.16 ------ iProver source info
% 2.41/1.16
% 2.41/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.41/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.41/1.16 git: non_committed_changes: false
% 2.41/1.16 git: last_make_outside_of_git: false
% 2.41/1.16
% 2.41/1.16 ------ Parsing...
% 2.41/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.41/1.16
% 2.41/1.16 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.41/1.16
% 2.41/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.41/1.16
% 2.41/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.16 ------ Proving...
% 2.41/1.16 ------ Problem Properties
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16 clauses 25
% 2.41/1.16 conjectures 1
% 2.41/1.16 EPR 11
% 2.41/1.16 Horn 22
% 2.41/1.16 unary 9
% 2.41/1.16 binary 9
% 2.41/1.16 lits 49
% 2.41/1.16 lits eq 10
% 2.41/1.16 fd_pure 0
% 2.41/1.16 fd_pseudo 0
% 2.41/1.16 fd_cond 1
% 2.41/1.16 fd_pseudo_cond 5
% 2.41/1.16 AC symbols 0
% 2.41/1.16
% 2.41/1.16 ------ Schedule dynamic 5 is on
% 2.41/1.16
% 2.41/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16 ------
% 2.41/1.16 Current options:
% 2.41/1.16 ------
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16 ------ Proving...
% 2.41/1.16
% 2.41/1.16
% 2.41/1.16 % SZS status Theorem for theBenchmark.p
% 2.41/1.16
% 2.41/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.16
% 2.41/1.16
%------------------------------------------------------------------------------