%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET930+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 : n006.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 02:49:08 PM UTC 2026
% Result : Theorem 0.77s 1.21s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 18 unt; 0 def)
% Number of atoms : 165 ( 94 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 183 ( 82 ~; 68 |; 29 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 114 !; 3 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& set_difference(unordered_pair(X0,X1),X2) != empty_set ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
( unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2)
& set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1)
& set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0)
& empty_set != set_difference(unordered_pair(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
| ( ~ in(X1,X2)
& ~ in(X0,X2) ) )
& ( in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
| ( ~ in(X1,X2)
& ~ in(X0,X2) ) )
& ( in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( empty_set != set_difference(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = empty_set ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( empty_set != set_difference(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = empty_set ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(flattening,[],[f18]) ).
fof(f22,plain,
unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
empty_set != set_difference(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( in(X1,X2)
| in(X0,X2)
| unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| empty_set = set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( X0 != X1
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f41,plain,
! [X2,X1] :
( in(X1,X2)
| singleton(X1) = set_difference(unordered_pair(X1,X1),X2) ),
inference(equality_resolution,[],[f36]) ).
tcf(c_49,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != empty_set,
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,negated_conjecture,
set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| in(X0,X2)
| ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1) ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),X1) = empty_set )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(unordered_pair(X2,X0),X1) = singleton(X2) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),X1) = singleton(X0) ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(equality_factoring,[status(thm)],[c_53]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X1,X1),X0) = singleton(X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X1,X1),X0) = singleton(X1) )
| ( set_difference(unordered_pair(X0,X0),X1) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_62,c_453]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != singleton(X1) ) ),
inference(superposition,[status(thm)],[c_56,c_63]) ).
tcf(c_683,plain,
( in(sK0,sK2)
| ( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) )
| ~ in(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_728,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(X0,X0),X0) = singleton(X0) )
| ( singleton(X0) != singleton(X0) ) ),
inference(equality_factoring,[status(thm)],[c_470]) ).
tcf(c_730,plain,
! [X0: $i] : set_difference(unordered_pair(X0,X0),X0) = singleton(X0),
inference(equality_resolution_simp,[status(thm)],[c_728]) ).
tcf(c_747,plain,
! [X0: $i] : ~ in(X0,X0),
inference(superposition,[status(thm)],[c_730,c_486]) ).
tcf(c_756,plain,
! [X0: $i] : set_difference(unordered_pair(X0,X0),X0) = unordered_pair(X0,X0),
inference(superposition,[status(thm)],[c_421,c_747]) ).
tcf(c_758,plain,
! [X0: $i] : unordered_pair(X0,X0) = singleton(X0),
inference(light_normalisation,[status(thm)],[c_756,c_730]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(demodulation,[status(thm)],[c_62,c_758]) ).
tcf(c_780,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( set_difference(singleton(X0),X1) != singleton(X0) ) ),
inference(superposition,[status(thm)],[c_758,c_55]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ( set_difference(singleton(X1),X2) = singleton(X1) )
| ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_767,c_61]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(singleton(X2),X1) = singleton(X2) )
| ( set_difference(unordered_pair(X2,X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_767,c_57]) ).
tcf(c_813,plain,
( in(sK1,sK2)
| in(sK0,sK2)
| ( set_difference(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(singleton(X3),X2) = singleton(X3) )
| ( set_difference(singleton(X1),X2) = singleton(X1) )
| ( set_difference(unordered_pair(X3,X0),X2) = empty_set )
| ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_797,c_798]) ).
tcf(c_3298,plain,
! [X0: $i] :
( ( set_difference(singleton(sK0),sK2) = singleton(sK0) )
| ( set_difference(singleton(X0),sK2) = singleton(X0) )
| ( set_difference(unordered_pair(sK1,X0),sK2) = singleton(sK1) ) ),
inference(superposition,[status(thm)],[c_1244,c_49]) ).
tcf(c_4030,plain,
! [X0: $i] :
( ( set_difference(singleton(sK0),sK2) = singleton(sK0) )
| ( set_difference(singleton(X0),sK2) = singleton(X0) )
| ( set_difference(unordered_pair(X0,sK1),sK2) = singleton(sK1) ) ),
inference(superposition,[status(thm)],[c_56,c_3298]) ).
tcf(c_4032,plain,
( ( set_difference(singleton(sK1),sK2) = singleton(sK1) )
| ( set_difference(singleton(sK0),sK2) = singleton(sK0) ) ),
inference(superposition,[status(thm)],[c_758,c_3298]) ).
tcf(c_4076,plain,
( ( set_difference(singleton(sK0),sK2) = singleton(sK0) )
| ( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK1) ) ),
inference(instantiation,[status(thm)],[c_4030]) ).
tcf(c_4095,plain,
set_difference(singleton(sK0),sK2) = singleton(sK0),
inference(global_subsumption_just,[status(thm)],[c_4032,c_51,c_4076]) ).
tcf(c_4098,plain,
~ in(sK0,sK2),
inference(superposition,[status(thm)],[c_4095,c_780]) ).
tcf(c_4101,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4098,c_813,c_683,c_52,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n006.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 12:23:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 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...
% 0.77/1.21 % SZS status Started for theBenchmark.p
% 0.77/1.21 % SZS status Theorem for theBenchmark.p
% 0.77/1.21
% 0.77/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.77/1.21
% 0.77/1.21 % ------ iProver source info
% 0.77/1.21
% 0.77/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.77/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.77/1.21 % git: non_committed_changes: false
% 0.77/1.21
% 0.77/1.21 % ------ Parsing...
% 0.77/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.77/1.21
% 0.77/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.77/1.21
% 0.77/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.77/1.21
% 0.77/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.77/1.21 % ------ Proving...
% 0.77/1.21 % ------ Problem Properties
% 0.77/1.21
% 0.77/1.21 %
% 0.77/1.21 % clauses 19
% 0.77/1.21 % conjectures 4
% 0.77/1.21 % EPR 4
% 0.77/1.21 % Horn 15
% 0.77/1.21 % unary 8
% 0.77/1.21 % binary 7
% 0.77/1.21 % lits 34
% 0.77/1.21 % lits eq 16
% 0.77/1.21 % fd_pure 0
% 0.77/1.21 % fd_pseudo 0
% 0.77/1.21 % fd_cond 0
% 0.77/1.21 % fd_pseudo_cond 1
% 0.77/1.21 % AC symbols 0
% 0.77/1.21
% 0.77/1.21 % ------ Schedule dynamic 5 is on
% 0.77/1.21
% 0.77/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.77/1.21
% 0.77/1.21
% 0.77/1.21 % ------
% 0.77/1.21 % Current options:
% 0.77/1.21 % ------
% 0.77/1.21
% 0.77/1.21
% 0.77/1.21 %
% 0.77/1.21
% 0.77/1.21 % ------ Proving...
% 0.77/1.21 %
% 0.77/1.21
% 0.77/1.21 % SZS status Theorem for theBenchmark.p
% 0.77/1.21
% 0.77/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.77/1.21
% 0.77/1.21
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