%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET695+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 02:47:49 PM UTC 2026
% Result : Theorem 4.38s 1.32s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 60 ( 4 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 76 ~; 83 |; 26 &)
% ( 5 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 85 !; 14 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> subset(difference(X2,X1),difference(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI24) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| subset(difference(X2,X1),difference(X2,X0)) )
& ( ~ subset(X0,X1)
| ~ subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| subset(difference(X2,X1),difference(X2,X0)) )
& ( ~ subset(X0,X1)
| ~ subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( subset(sK1,sK2)
& subset(sK0,sK2)
& ( subset(sK0,sK1)
| subset(difference(sK2,sK1),difference(sK2,sK0)) )
& ( ~ subset(sK0,sK1)
| ~ subset(difference(sK2,sK1),difference(sK2,sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f23]) ).
fof(f26,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
( subset(sK0,sK1)
| subset(difference(sK2,sK1),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
( ~ subset(sK0,sK1)
| ~ subset(difference(sK2,sK1),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK0,sK1)
| ~ subset(difference(sK2,sK1),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,negated_conjecture,
( subset(sK0,sK1)
| subset(difference(sK2,sK1),difference(sK2,sK0)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,negated_conjecture,
subset(sK0,sK2),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_143,plain,
( subset(sK0,sK1)
| ~ member(sK3(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_144,plain,
( subset(sK0,sK1)
| member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_145,plain,
( subset(difference(sK2,sK1),difference(sK2,sK0))
| member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_146,plain,
( subset(difference(sK2,sK1),difference(sK2,sK0))
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_151,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_156,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_157,plain,
( member(sK3(sK0,sK1),sK2)
| ~ subset(sK0,sK2)
| ~ member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_160,plain,
! [X0: $i] :
( ~ member(sK3(sK0,sK1),sK0)
| ~ member(sK3(sK0,sK1),difference(X0,sK0)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_161,plain,
( ~ member(sK3(sK0,sK1),sK0)
| ~ member(sK3(sK0,sK1),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_169,plain,
! [X0: $i] :
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X0)
| member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,X0))
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X1)
| ~ subset(X0,X1)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X1)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_231,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_178]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X1)
| ~ subset(X0,X1)
| ~ member(sK3(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X1)
| member(sK3(sK0,sK1),difference(X0,X1))
| ~ member(sK3(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),difference(X1,sK0))
| ~ member(sK3(sK0,sK1),X0)
| ~ subset(X0,difference(X1,sK0)) ),
inference(instantiation,[status(thm)],[c_287]) ).
tcf(c_437,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),sK1)
| member(sK3(sK0,sK1),difference(X0,sK1))
| ~ member(sK3(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_288]) ).
tcf(c_438,plain,
( member(sK3(sK0,sK1),sK1)
| member(sK3(sK0,sK1),difference(sK2,sK1))
| ~ member(sK3(sK0,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_437]) ).
tcf(c_531,plain,
( member(sK3(sK0,sK1),difference(sK2,sK0))
| ~ member(sK3(sK0,sK1),difference(sK2,sK1))
| ~ subset(difference(sK2,sK1),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| member(sK3(X0,X3),X1)
| ~ subset(X0,difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_326,c_57]) ).
tcf(c_770,plain,
! [X0: $i] :
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1)
| ~ subset(X0,sK1)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X0) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_799,plain,
! [X0: $i] :
( subset(sK0,sK1)
| subset(difference(sK2,sK1),X0)
| member(sK3(difference(sK2,sK1),X0),sK2) ),
inference(superposition,[status(thm)],[c_50,c_556]) ).
tcf(c_807,plain,
subset(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_799,c_51,c_50,c_143,c_144,c_157,c_161,c_438,c_531]) ).
tcf(c_1156,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0) ),
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1875,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0)
| member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK0))
| ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2) ),
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_1879,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1875,c_1156,c_807,c_231,c_151,c_145,c_146,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET695+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 11:44:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 4.38/1.32 % SZS status Started for theBenchmark.p
% 4.38/1.32 % SZS status Theorem for theBenchmark.p
% 4.38/1.32
% 4.38/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.38/1.32
% 4.38/1.32 % ------ iProver source info
% 4.38/1.32
% 4.38/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.38/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.38/1.32 % git: non_committed_changes: false
% 4.38/1.32
% 4.38/1.32 % ------ Parsing...
% 4.38/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.38/1.32
% 4.38/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.38/1.32
% 4.38/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.38/1.32 % ------ Proving...
% 4.38/1.32 % ------ Problem Properties
% 4.38/1.32
% 4.38/1.32 %
% 4.38/1.32 % clauses 10
% 4.38/1.32 % conjectures 4
% 4.38/1.32 % EPR 3
% 4.38/1.32 % Horn 7
% 4.38/1.32 % unary 2
% 4.38/1.32 % binary 6
% 4.38/1.32 % lits 20
% 4.38/1.32 % lits eq 0
% 4.38/1.32 % fd_pure 0
% 4.38/1.32 % fd_pseudo 0
% 4.38/1.32 % fd_cond 0
% 4.38/1.32 % fd_pseudo_cond 0
% 4.38/1.32 % AC symbols 0
% 4.38/1.32
% 4.38/1.32 % ------ Schedule dynamic 5 is on
% 4.38/1.32
% 4.38/1.32 % ------ no equalities: superposition off
% 4.38/1.32
% 4.38/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.38/1.32
% 4.38/1.32
% 4.38/1.32 % ------
% 4.38/1.32 % Current options:
% 4.38/1.32 % ------
% 4.38/1.32
% 4.38/1.32
% 4.38/1.32 %
% 4.38/1.32
% 4.38/1.32 % ------ Proving...
% 4.38/1.32 %
% 4.38/1.32
% 4.38/1.32 % SZS status Theorem for theBenchmark.p
% 4.38/1.32
% 4.38/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.38/1.32
% 4.38/1.32
%------------------------------------------------------------------------------