%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET958+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 : n011.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 02:49:12 PM UTC 2026
% Result : Theorem 0.42s 1.22s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 106 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 50 ~; 37 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 83 !; 10 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,conjecture,
! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
~ ! [X0,X1] :
( ( ! [X5,X6] :
( in(ordered_pair(X5,X6),X0)
=> in(ordered_pair(X5,X6),X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> subset(X0,X1) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
? [X0,X1] :
( ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),X0)
| in(ordered_pair(X5,X6),X1) )
& ! [X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X2
| ~ in(X2,X0) )
& ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
? [X0,X1] :
( ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),X0)
| in(ordered_pair(X5,X6),X1) )
& ! [X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X2
| ~ in(X2,X0) )
& ~ subset(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f14]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f22,plain,
( ! [X5,X6] :
( ~ in(ordered_pair(X5,X6),sK3)
| in(ordered_pair(X5,X6),sK4) )
& ! [X2] :
( ordered_pair(sK5(X2),sK6(X2)) = X2
| ~ in(X2,sK3) )
& ~ subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X3,sK5(X2)),skolemize(X4,sK6(X2))],[f16]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f33,plain,
! [X6,X5] :
( ~ in(ordered_pair(X5,X6),sK3)
| in(ordered_pair(X5,X6),sK4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2] :
( ordered_pair(sK5(X2),sK6(X2)) = X2
| ~ in(X2,sK3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
~ subset(sK3,sK4),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X2] :
( unordered_pair(unordered_pair(sK5(X2),sK6(X2)),singleton(sK5(X2))) = X2
| ~ in(X2,sK3) ),
inference(definition_unfolding,[],[f34,f28]) ).
fof(f38,plain,
! [X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK3)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4) ),
inference(definition_unfolding,[],[f33,f28,f28]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_58,negated_conjecture,
~ subset(sK3,sK4),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK5(X0),sK6(X0)),singleton(sK5(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_121,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK5(X0)),unordered_pair(sK5(X0),sK6(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_59,c_50]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(demodulation,[status(thm)],[c_60,c_50]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_58]) ).
tcf(c_179,plain,
in(sK0(sK3,sK4),sK3),
inference(unflattening,[status(thm)],[c_178]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ in(sK0(X0,X1),X1)
| ( X1 != sK4 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_58]) ).
tcf(c_184,plain,
~ in(sK0(sK3,sK4),sK4),
inference(unflattening,[status(thm)],[c_183]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_205,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK5(X0)),unordered_pair(sK5(X0),sK6(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_206,negated_conjecture,
~ subset(sK3,sK4),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_401,plain,
! [X0: $i] :
( subset(sK3,X0)
| ( unordered_pair(singleton(sK5(sK0(sK3,X0))),unordered_pair(sK5(sK0(sK3,X0)),sK6(sK0(sK3,X0)))) = sK0(sK3,X0) ) ),
inference(superposition,[status(thm)],[c_52,c_205]) ).
tcf(c_469,plain,
unordered_pair(singleton(sK5(sK0(sK3,sK4))),unordered_pair(sK5(sK0(sK3,sK4)),sK6(sK0(sK3,sK4)))) = sK0(sK3,sK4),
inference(superposition,[status(thm)],[c_401,c_206]) ).
tcf(c_475,plain,
( in(unordered_pair(singleton(sK5(sK0(sK3,sK4))),unordered_pair(sK5(sK0(sK3,sK4)),sK6(sK0(sK3,sK4)))),sK4)
| ~ in(sK0(sK3,sK4),sK3) ),
inference(superposition,[status(thm)],[c_469,c_204]) ).
tcf(c_476,plain,
( in(sK0(sK3,sK4),sK4)
| ~ in(sK0(sK3,sK4),sK3) ),
inference(light_normalisation,[status(thm)],[c_475,c_469]) ).
tcf(c_484,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_476,c_184,c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:26:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.16/0.43
% 0.16/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.43
% 0.16/0.43 % Detected problem language: tptp
% 0.16/0.46 % Proving...
% 0.42/1.22 % SZS status Started for theBenchmark.p
% 0.42/1.22 % SZS status Theorem for theBenchmark.p
% 0.42/1.22
% 0.42/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/1.22
% 0.42/1.22 % ------ iProver source info
% 0.42/1.22
% 0.42/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/1.22 % git: non_committed_changes: false
% 0.42/1.22
% 0.42/1.22 % ------ Parsing...
% 0.42/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.42/1.22
% 0.42/1.22 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.42/1.22
% 0.42/1.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.42/1.22
% 0.42/1.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.42/1.22 % ------ Proving...
% 0.42/1.22 % ------ Problem Properties
% 0.42/1.22
% 0.42/1.22 %
% 0.42/1.22 % clauses 12
% 0.42/1.22 % conjectures 1
% 0.42/1.22 % EPR 6
% 0.42/1.22 % Horn 11
% 0.42/1.22 % unary 6
% 0.42/1.22 % binary 5
% 0.42/1.22 % lits 19
% 0.42/1.22 % lits eq 2
% 0.42/1.22 % fd_pure 0
% 0.42/1.22 % fd_pseudo 0
% 0.42/1.22 % fd_cond 0
% 0.42/1.22 % fd_pseudo_cond 0
% 0.42/1.22 % AC symbols 0
% 0.42/1.22
% 0.42/1.22 % ------ Schedule dynamic 5 is on
% 0.42/1.22
% 0.42/1.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/1.22
% 0.42/1.22
% 0.42/1.22 % ------
% 0.42/1.22 % Current options:
% 0.42/1.22 % ------
% 0.42/1.22
% 0.42/1.22
% 0.42/1.22 %
% 0.42/1.22
% 0.42/1.22 % ------ Proving...
% 0.42/1.22 %
% 0.42/1.22
% 0.42/1.22 % SZS status Theorem for theBenchmark.p
% 0.42/1.22
% 0.42/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.22
% 0.42/1.22
%------------------------------------------------------------------------------