%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU125+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:29 PM UTC 2026
% Result : Theorem 1.76s 1.29s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 149 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 175 ( 64 ~; 70 |; 34 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 67 !; 11 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f44,plain,
? [X0,X1,X2] :
( subset(X2,X1)
& subset(X0,X1)
& ~ subset(set_union2(X0,X2),X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f45,plain,
? [X0,X1,X2] :
( subset(X2,X1)
& subset(X0,X1)
& ~ subset(set_union2(X0,X2),X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
( subset(sK4,sK3)
& subset(sK2,sK3)
& ~ subset(set_union2(sK2,sK4),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f45]) ).
fof(f57,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,[],[f46]) ).
fof(f58,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,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK5(X0,X1),X0)
& ~ in(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f58]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),X1)
| in(sK7(X0,X1,X2),X0) )
& ( ~ in(sK7(X0,X1,X2),X2)
| ( ~ in(sK7(X0,X1,X2),X1)
& ~ in(sK7(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f67]) ).
fof(f85,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f56]) ).
fof(f86,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f56]) ).
fof(f87,plain,
~ subset(set_union2(sK2,sK4),sK3),
inference(cnf_transformation,[],[f56]) ).
fof(f89,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f90,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f91,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f101,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f131,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f101]) ).
tcf(c_58,negated_conjecture,
~ subset(set_union2(sK2,sK4),sK3),
inference(cnf_transformation,[],[f87]) ).
tcf(c_59,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f86]) ).
tcf(c_60,negated_conjecture,
subset(sK4,sK3),
inference(cnf_transformation,[],[f85]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_2204,plain,
( subset(set_union2(sK2,sK4),sK3)
| ~ in(sK5(set_union2(sK2,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2205,plain,
( subset(set_union2(sK2,sK4),sK3)
| in(sK5(set_union2(sK2,sK4),sK3),set_union2(sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2288,plain,
( in(sK5(set_union2(sK2,sK4),sK3),sK4)
| in(sK5(set_union2(sK2,sK4),sK3),sK2)
| ~ in(sK5(set_union2(sK2,sK4),sK3),set_union2(sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_2740,plain,
! [X0: $i] :
( in(sK5(set_union2(sK2,sK4),sK3),X0)
| ~ subset(sK2,X0)
| ~ in(sK5(set_union2(sK2,sK4),sK3),sK2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3699,plain,
! [X0: $i] :
( in(sK5(set_union2(sK2,sK4),sK3),X0)
| ~ subset(sK4,X0)
| ~ in(sK5(set_union2(sK2,sK4),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_7698,plain,
( in(sK5(set_union2(sK2,sK4),sK3),sK3)
| ~ subset(sK2,sK3)
| ~ in(sK5(set_union2(sK2,sK4),sK3),sK2) ),
inference(instantiation,[status(thm)],[c_2740]) ).
tcf(c_9163,plain,
( in(sK5(set_union2(sK2,sK4),sK3),sK3)
| ~ subset(sK4,sK3)
| ~ in(sK5(set_union2(sK2,sK4),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_3699]) ).
tcf(c_9164,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9163,c_7698,c_2288,c_2205,c_2204,c_58,c_59,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:49:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.76/1.29 % SZS status Started for theBenchmark.p
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.76/1.29
% 1.76/1.29 % ------ iProver source info
% 1.76/1.29
% 1.76/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.76/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.76/1.29 % git: non_committed_changes: false
% 1.76/1.29
% 1.76/1.29 % ------ Parsing...
% 1.76/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 % ------ Problem Properties
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29 % clauses 48
% 1.76/1.29 % conjectures 3
% 1.76/1.29 % EPR 18
% 1.76/1.29 % Horn 39
% 1.76/1.29 % unary 15
% 1.76/1.29 % binary 20
% 1.76/1.29 % lits 96
% 1.76/1.29 % lits eq 18
% 1.76/1.29 % fd_pure 0
% 1.76/1.29 % fd_pseudo 0
% 1.76/1.29 % fd_cond 3
% 1.76/1.29 % fd_pseudo_cond 8
% 1.76/1.29 % AC symbols 0
% 1.76/1.29
% 1.76/1.29 % ------ Schedule dynamic 5 is on
% 1.76/1.29
% 1.76/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 % ------
% 1.76/1.29 % Current options:
% 1.76/1.29 % ------
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.29
% 1.76/1.29
%------------------------------------------------------------------------------