%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET932+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 02:49:09 PM UTC 2026
% Result : Theorem 2.41s 1.28s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 10 unt; 2 def)
% Number of atoms : 136 ( 11 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 131 ( 51 ~; 54 |; 18 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 75 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f8,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(powerset(X0),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(powerset(X0),powerset(X1)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
? [X0,X1] :
( subset(X0,X1)
& ~ subset(powerset(X0),powerset(X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| subset(sK0(X0,X1),X0) )
& ( ~ in(sK0(X0,X1),X1)
| ~ subset(sK0(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f20]) ).
fof(f24,plain,
( subset(sK4,sK5)
& ~ subset(powerset(sK4),powerset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f15]) ).
fof(f26,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
~ subset(powerset(sK4),powerset(sK5)),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f27]) ).
fof(f40,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,negated_conjecture,
~ subset(powerset(sK4),powerset(sK5)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f37]) ).
tcf(c_355,definition,
iPr_def_10 = powerset(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_356,definition,
iPr_def_11 = powerset(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_357,negated_conjecture,
subset(sK4,sK5),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_358,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_61,c_356,c_355]) ).
tcf(c_654,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,sK5) ),
inference(superposition,[status(thm)],[c_356,c_52]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK1(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_805,plain,
! [X0: $i] :
( subset(X0,sK5)
| ~ subset(X0,sK4) ),
inference(superposition,[status(thm)],[c_357,c_60]) ).
tcf(c_890,plain,
! [X0: $i] :
( subset(powerset(sK4),X0)
| subset(sK1(powerset(sK4),X0),sK5) ),
inference(superposition,[status(thm)],[c_692,c_805]) ).
tcf(c_891,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| subset(sK1(iPr_def_10,X0),sK5) ),
inference(light_normalisation,[status(thm)],[c_890,c_355]) ).
tcf(c_934,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK1(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_891,c_654]) ).
tcf(c_978,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_934,c_54]) ).
tcf(c_980,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_978,c_358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET932+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:21:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.41/1.28 % SZS status Started for theBenchmark.p
% 2.41/1.28 % SZS status Theorem for theBenchmark.p
% 2.41/1.28
% 2.41/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.28
% 2.41/1.28 % ------ iProver source info
% 2.41/1.28
% 2.41/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.28 % git: non_committed_changes: false
% 2.41/1.28
% 2.41/1.28 % ------ Parsing...
% 2.41/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/1.28
% 2.41/1.28 % ------ Preprocessing... sup_sim: 0 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 %
% 2.41/1.28
% 2.41/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/1.28
% 2.41/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.28 % ------ Proving...
% 2.41/1.28 % ------ Problem Properties
% 2.41/1.28
% 2.41/1.28 %
% 2.41/1.28 % clauses 15
% 2.41/1.28 % conjectures 2
% 2.41/1.28 % EPR 7
% 2.41/1.28 % Horn 13
% 2.41/1.28 % unary 6
% 2.41/1.28 % binary 5
% 2.41/1.28 % lits 28
% 2.41/1.28 % lits eq 5
% 2.41/1.28 % fd_pure 0
% 2.41/1.28 % fd_pseudo 0
% 2.41/1.28 % fd_cond 0
% 2.41/1.28 % fd_pseudo_cond 2
% 2.41/1.28 % AC symbols 0
% 2.41/1.28
% 2.41/1.28 % ------ Schedule dynamic 5 is on
% 2.41/1.28
% 2.41/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.28
% 2.41/1.28
% 2.41/1.28 % ------
% 2.41/1.28 % Current options:
% 2.41/1.28 % ------
% 2.41/1.28
% 2.41/1.28
% 2.41/1.28 %
% 2.41/1.28
% 2.41/1.28 % ------ Proving...
% 2.41/1.28 %
% 2.41/1.28
% 2.41/1.28 % SZS status Theorem for theBenchmark.p
% 2.41/1.28
% 2.41/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.28
% 2.41/1.28
%------------------------------------------------------------------------------