TSTP Solution File: SET610+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET610+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 15:08:37 EDT 2023
% Result : Theorem 0.86s 1.17s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 129 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 140 ( 57 ~; 63 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 4 sgn; 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f9,conjecture,
! [X0,X1] : difference(X0,X1) = difference(union(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th83) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : difference(X0,X1) = difference(union(X0,X1),X1),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
<~> member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
? [X0,X1] : difference(X0,X1) != difference(union(X0,X1),X1),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) )
& ( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) )
& ( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f31,plain,
( ? [X0,X1] : difference(X0,X1) != difference(union(X0,X1),X1)
=> difference(sK3,sK4) != difference(union(sK3,sK4),sK4) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
difference(sK3,sK4) != difference(union(sK3,sK4),sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f31]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f53,plain,
difference(sK3,sK4) != difference(union(sK3,sK4),sK4),
inference(cnf_transformation,[],[f32]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_50,plain,
( X0 = X1
| member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_52,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_53,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_55,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_56,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_67,negated_conjecture,
difference(union(sK3,sK4),sK4) != difference(sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
cnf(c_560,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(union(sK3,sK4),sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_743,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_825,plain,
( member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(union(sK3,sK4),sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_50,c_67]) ).
cnf(c_847,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK4)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_825,c_55]) ).
cnf(c_896,plain,
~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_847,c_55]) ).
cnf(c_1314,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(union(sK3,sK4),X0))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_1319,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(union(sK3,sK4),sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[c_1314]) ).
cnf(c_1321,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1652,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(union(sK3,sK4),sK4))
| ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_49,c_67]) ).
cnf(c_2622,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,X0))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_2623,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,X0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_2626,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_2623]) ).
cnf(c_2627,plain,
( ~ member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK3)
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),difference(sK3,sK4))
| member(sK0(difference(union(sK3,sK4),sK4),difference(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[c_2622]) ).
cnf(c_3089,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2627,c_2626,c_1652,c_1321,c_1319,c_896,c_825,c_743,c_560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET610+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:13:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.86/1.17 % SZS status Started for theBenchmark.p
% 0.86/1.17 % SZS status Theorem for theBenchmark.p
% 0.86/1.17
% 0.86/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.86/1.17
% 0.86/1.17 ------ iProver source info
% 0.86/1.17
% 0.86/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.86/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.86/1.17 git: non_committed_changes: false
% 0.86/1.17 git: last_make_outside_of_git: false
% 0.86/1.17
% 0.86/1.17 ------ Parsing...
% 0.86/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.86/1.17
% 0.86/1.17 ------ Preprocessing... sup_sim: 0 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
% 0.86/1.17
% 0.86/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.86/1.17
% 0.86/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.86/1.17 ------ Proving...
% 0.86/1.17 ------ Problem Properties
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17 clauses 17
% 0.86/1.17 conjectures 1
% 0.86/1.17 EPR 3
% 0.86/1.17 Horn 12
% 0.86/1.17 unary 3
% 0.86/1.17 binary 6
% 0.86/1.17 lits 39
% 0.86/1.17 lits eq 7
% 0.86/1.17 fd_pure 0
% 0.86/1.17 fd_pseudo 0
% 0.86/1.17 fd_cond 0
% 0.86/1.17 fd_pseudo_cond 5
% 0.86/1.17 AC symbols 0
% 0.86/1.17
% 0.86/1.17 ------ Input Options Time Limit: Unbounded
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17 ------
% 0.86/1.17 Current options:
% 0.86/1.17 ------
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17 ------ Proving...
% 0.86/1.17
% 0.86/1.17
% 0.86/1.17 % SZS status Theorem for theBenchmark.p
% 0.86/1.17
% 0.86/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.86/1.17
% 0.86/1.17
%------------------------------------------------------------------------------