%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:48:38 PM UTC 2026
% Result : Theorem 3.69s 1.10s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 21 ~; 17 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 36 !; 1 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f19,axiom,
! [X0,X1] :
( member(X1,suc(X0))
<=> member(X1,union(X0,singleton(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',successor) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV12) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
? [X0] :
( member(X0,on)
& ~ member(X0,suc(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f35,plain,
( member(sK1,on)
& ~ member(sK1,suc(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( ( ~ member(X1,suc(X0))
| member(X1,union(X0,singleton(X0))) )
& ( ~ member(X1,union(X0,singleton(X0)))
| member(X1,suc(X0)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( ~ member(X0,singleton(X1))
| X0 = X1 )
& ( X0 != X1
| member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f64,plain,
~ member(sK1,suc(sK1)),
inference(cnf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0,X1] :
( ~ member(X1,union(X0,singleton(X0)))
| member(X1,suc(X0)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f106,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f87]) ).
tcf(c_49,negated_conjecture,
~ member(sK1,suc(sK1)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,suc(X1))
| ~ member(X0,union(X1,singleton(X1))) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_72,plain,
! [X0: $i] : member(X0,singleton(X0)),
inference(cnf_transformation,[],[f106]) ).
tcf(c_3632,plain,
! [X0: $i,X1: $i] :
( member(X0,suc(X1))
| ~ member(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_70,c_56]) ).
tcf(c_3805,plain,
! [X0: $i] : member(X0,suc(X0)),
inference(superposition,[status(thm)],[c_72,c_3632]) ).
tcf(c_3821,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_3805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:04:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.69/1.10 % SZS status Started for theBenchmark.p
% 3.69/1.10 % SZS status Theorem for theBenchmark.p
% 3.69/1.10
% 3.69/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/1.10
% 3.69/1.10 % ------ iProver source info
% 3.69/1.10
% 3.69/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/1.10 % git: non_committed_changes: false
% 3.69/1.10
% 3.69/1.10 % ------ Parsing...
% 3.69/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.69/1.10
% 3.69/1.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.69/1.10
% 3.69/1.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.69/1.10
% 3.69/1.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.10 % ------ Proving...
% 3.69/1.10 % ------ Problem Properties
% 3.69/1.10
% 3.69/1.10 %
% 3.69/1.10 % clauses 43
% 3.69/1.10 % conjectures 2
% 3.69/1.10 % EPR 14
% 3.69/1.10 % Horn 27
% 3.69/1.10 % unary 3
% 3.69/1.10 % binary 20
% 3.69/1.10 % lits 113
% 3.69/1.10 % lits eq 3
% 3.69/1.10 % fd_pure 0
% 3.69/1.10 % fd_pseudo 0
% 3.69/1.10 % fd_cond 0
% 3.69/1.10 % fd_pseudo_cond 2
% 3.69/1.10 % AC symbols 0
% 3.69/1.10
% 3.69/1.10 % ------ Schedule dynamic 5 is on
% 3.69/1.10
% 3.69/1.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.10
% 3.69/1.10
% 3.69/1.10 % ------
% 3.69/1.10 % Current options:
% 3.69/1.10 % ------
% 3.69/1.10
% 3.69/1.10
% 3.69/1.10 %
% 3.69/1.10
% 3.69/1.10 % ------ Proving...
% 3.69/1.10 %
% 3.69/1.10
% 3.69/1.10 % SZS status Theorem for theBenchmark.p
% 3.69/1.10
% 3.69/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.10
% 3.69/1.10
%------------------------------------------------------------------------------