%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU229+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:56:15 PM UTC 2026
% Result : Theorem 4.05s 1.28s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 73 ( 24 unt; 0 def)
% Number of atoms : 234 ( 103 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 266 ( 105 ~; 112 |; 44 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 184 ( 0 sgn 176 !; 8 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2,X3] :
( X3 = unordered_triple(X0,X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ~ ( X4 != X2
& X4 != X1
& X4 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
fof(f6,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,conjecture,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f23,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f26,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( X3 = unordered_triple(X0,X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f42,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
? [X0,X1,X2] :
( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) != X3
| ! [X4] :
( ( ~ in(X4,X3)
| X2 = X4
| X1 = X4
| X0 = X4 )
& ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( in(X4,X3)
| X2 = X4
| X1 = X4
| X0 = X4 )
& ( ~ in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) ) )
| X3 = unordered_triple(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) != X3
| ! [X4] :
( ( ~ in(X4,X3)
| X2 = X4
| X1 = X4
| X0 = X4 )
& ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( in(X4,X3)
| X2 = X4
| X1 = X4
| X0 = X4 )
& ( ~ in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) ) )
| X3 = unordered_triple(X0,X1,X2) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) != X3
| ! [X5] :
( ( ~ in(X5,X3)
| X2 = X5
| X1 = X5
| X0 = X5 )
& ( ( X2 != X5
& X1 != X5
& X0 != X5 )
| in(X5,X3) ) ) )
& ( ? [X4] :
( ( in(X4,X3)
| X2 = X4
| X1 = X4
| X0 = X4 )
& ( ~ in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) ) )
| X3 = unordered_triple(X0,X1,X2) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) != X3
| ! [X5] :
( ( ~ in(X5,X3)
| X2 = X5
| X1 = X5
| X0 = X5 )
& ( ( X2 != X5
& X1 != X5
& X0 != X5 )
| in(X5,X3) ) ) )
& ( ( ( in(sK0(X0,X1,X2,X3),X3)
| sK0(X0,X1,X2,X3) = X2
| sK0(X0,X1,X2,X3) = X1
| sK0(X0,X1,X2,X3) = X0 )
& ( ~ in(sK0(X0,X1,X2,X3),X3)
| ( sK0(X0,X1,X2,X3) != X2
& sK0(X0,X1,X2,X3) != X1
& sK0(X0,X1,X2,X3) != X0 ) ) )
| X3 = unordered_triple(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0(X0,X1,X2,X3))],[f50]) ).
fof(f52,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f6]) ).
fof(f63,plain,
( in(sK14,sK12)
& in(sK13,sK14)
& in(sK12,sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f43]) ).
fof(f64,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK15(X1))
| ~ in(X3,X1) )
& in(sK15(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X2,sK15(X1))],[f46]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X5] :
( unordered_triple(X0,X1,X2) != X3
| ~ in(X5,X3)
| X2 = X5
| X1 = X5
| X0 = X5 ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X5] :
( unordered_triple(X0,X1,X2) != X3
| X2 != X5
| in(X5,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X5] :
( unordered_triple(X0,X1,X2) != X3
| X1 != X5
| in(X5,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X5] :
( unordered_triple(X0,X1,X2) != X3
| X0 != X5
| in(X5,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f52]) ).
fof(f103,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f104,plain,
in(sK14,sK12),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
in(sK13,sK14),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
in(sK12,sK13),
inference(cnf_transformation,[],[f63]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f109,plain,
! [X3,X0,X1] :
( ~ in(X3,sK15(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f110,plain,
! [X0,X1] :
( in(sK15(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
! [X2,X3,X1,X5] :
( unordered_triple(X5,X1,X2) != X3
| in(X5,X3) ),
inference(equality_resolution,[],[f73]) ).
fof(f113,plain,
! [X2,X1,X5] : in(X5,unordered_triple(X5,X1,X2)),
inference(equality_resolution,[],[f112]) ).
fof(f114,plain,
! [X2,X3,X0,X5] :
( unordered_triple(X0,X5,X2) != X3
| in(X5,X3) ),
inference(equality_resolution,[],[f72]) ).
fof(f115,plain,
! [X2,X0,X5] : in(X5,unordered_triple(X0,X5,X2)),
inference(equality_resolution,[],[f114]) ).
fof(f116,plain,
! [X3,X0,X1,X5] :
( unordered_triple(X0,X1,X5) != X3
| in(X5,X3) ),
inference(equality_resolution,[],[f71]) ).
fof(f117,plain,
! [X0,X1,X5] : in(X5,unordered_triple(X0,X1,X5)),
inference(equality_resolution,[],[f116]) ).
fof(f118,plain,
! [X2,X0,X1,X5] :
( ~ in(X5,unordered_triple(X0,X1,X2))
| X2 = X5
| X1 = X5
| X0 = X5 ),
inference(equality_resolution,[],[f70]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,unordered_triple(X0,X1,X2)),
inference(cnf_transformation,[],[f113]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,unordered_triple(X1,X0,X2)),
inference(cnf_transformation,[],[f115]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,unordered_triple(X1,X2,X0)),
inference(cnf_transformation,[],[f117]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_60,plain,
! [X0: $i] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f78]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_86,negated_conjecture,
in(sK12,sK13),
inference(cnf_transformation,[],[f106]) ).
tcf(c_87,negated_conjecture,
in(sK13,sK14),
inference(cnf_transformation,[],[f105]) ).
tcf(c_88,negated_conjecture,
in(sK14,sK12),
inference(cnf_transformation,[],[f104]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| ~ in(X0,sK15(X1)) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(X1,X2)
| ( X0 != X2 )
| ( sK1(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_85]) ).
tcf(c_332,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(X0),X0) ),
inference(unflattening,[status(thm)],[c_331]) ).
tcf(c_504,negated_conjecture,
in(sK14,sK12),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_505,negated_conjecture,
in(sK13,sK14),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_506,negated_conjecture,
in(sK12,sK13),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(unordered_triple(X0,X1,X2)),
inference(superposition,[status(thm)],[c_56,c_90]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i] : in(sK15(unordered_triple(X0,X1,X2)),unordered_triple(X0,X1,X2)),
inference(superposition,[status(thm)],[c_56,c_91]) ).
tcf(c_793,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(X0),X0) ),
inference(superposition,[status(thm)],[c_332,c_91]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(unordered_triple(X0,X1,X2))
| ( sK15(unordered_triple(X0,X1,X2)) = X2 )
| ( sK15(unordered_triple(X0,X1,X2)) = X1 )
| ( sK15(unordered_triple(X0,X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_793,c_59]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(unordered_triple(X0,X1,X2)) = X2 )
| ( sK15(unordered_triple(X0,X1,X2)) = X1 )
| ( sK15(unordered_triple(X0,X1,X2)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_847,c_775]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK15(unordered_triple(X1,X2,X3)) = X2 )
| ( sK15(unordered_triple(X1,X2,X3)) = X1 )
| ~ in(X0,X3)
| ~ in(X4,unordered_triple(X1,X2,X3))
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_854,c_92]) ).
tcf(c_6828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK15(unordered_triple(X1,X2,X3)) = X2 )
| ( sK15(unordered_triple(X1,X2,X3)) = X1 )
| ~ in(X1,X3)
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_56,c_971]) ).
tcf(c_6873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(unordered_triple(X0,X2,X1)) = X2 )
| ( sK15(unordered_triple(X0,X2,X1)) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_787,c_6828]) ).
tcf(c_6981,plain,
! [X0: $i] :
( ( sK15(unordered_triple(sK12,X0,sK13)) = sK12 )
| ( sK15(unordered_triple(sK12,X0,sK13)) = X0 ) ),
inference(superposition,[status(thm)],[c_506,c_6873]) ).
tcf(c_7089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK15(unordered_triple(sK12,X1,sK13)) = X1 )
| ~ in(X0,sK12)
| ~ in(X2,unordered_triple(sK12,X1,sK13))
| ~ in(X0,unordered_triple(sK12,X1,sK13)) ),
inference(superposition,[status(thm)],[c_6981,c_92]) ).
tcf(c_9042,plain,
! [X0: $i,X1: $i] :
( ( sK15(unordered_triple(sK12,X1,sK13)) = X1 )
| ~ in(X1,sK12)
| ~ in(X0,unordered_triple(sK12,X1,sK13)) ),
inference(superposition,[status(thm)],[c_57,c_7089]) ).
tcf(c_9163,plain,
! [X0: $i] :
( ( sK15(unordered_triple(sK12,X0,sK13)) = X0 )
| ~ in(X0,sK12) ),
inference(superposition,[status(thm)],[c_787,c_9042]) ).
tcf(c_9214,plain,
sK15(unordered_triple(sK12,sK14,sK13)) = sK14,
inference(superposition,[status(thm)],[c_504,c_9163]) ).
tcf(c_9266,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,sK14)
| ~ in(X1,unordered_triple(sK12,sK14,sK13))
| ~ in(X0,unordered_triple(sK12,sK14,sK13)) ),
inference(superposition,[status(thm)],[c_9214,c_92]) ).
tcf(c_9492,plain,
! [X0: $i] :
( ~ in(sK13,sK14)
| ~ in(X0,unordered_triple(sK12,sK14,sK13)) ),
inference(superposition,[status(thm)],[c_58,c_9266]) ).
tcf(c_9496,plain,
! [X0: $i] : ~ in(X0,unordered_triple(sK12,sK14,sK13)),
inference(forward_subsumption_resolution,[status(thm)],[c_9492,c_505]) ).
tcf(c_9499,plain,
$false,
inference(superposition,[status(thm)],[c_56,c_9496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU229+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 13:16:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.05/1.28 % SZS status Started for theBenchmark.p
% 4.05/1.28 % SZS status Theorem for theBenchmark.p
% 4.05/1.28
% 4.05/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.05/1.28
% 4.05/1.28 % ------ iProver source info
% 4.05/1.28
% 4.05/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.05/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.05/1.28 % git: non_committed_changes: false
% 4.05/1.28
% 4.05/1.28 % ------ Parsing...
% 4.05/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.05/1.28
% 4.05/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 4.05/1.28
% 4.05/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.05/1.28
% 4.05/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.05/1.28 % ------ Proving...
% 4.05/1.28 % ------ Problem Properties
% 4.05/1.28
% 4.05/1.28 %
% 4.05/1.28 % clauses 24
% 4.05/1.28 % conjectures 3
% 4.05/1.28 % EPR 13
% 4.05/1.28 % Horn 21
% 4.05/1.28 % unary 12
% 4.05/1.28 % binary 5
% 4.05/1.28 % lits 46
% 4.05/1.28 % lits eq 15
% 4.05/1.28 % fd_pure 0
% 4.05/1.28 % fd_pseudo 0
% 4.05/1.28 % fd_cond 1
% 4.05/1.28 % fd_pseudo_cond 5
% 4.05/1.28 % AC symbols 0
% 4.05/1.28
% 4.05/1.28 % ------ Schedule dynamic 5 is on
% 4.05/1.28
% 4.05/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.05/1.28
% 4.05/1.28
% 4.05/1.28 % ------
% 4.05/1.28 % Current options:
% 4.05/1.28 % ------
% 4.05/1.28
% 4.05/1.28
% 4.05/1.28 %
% 4.05/1.28
% 4.05/1.28 % ------ Proving...
% 4.05/1.28 %
% 4.05/1.28
% 4.05/1.28 % SZS status Theorem for theBenchmark.p
% 4.05/1.28
% 4.05/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.28
% 4.05/1.28
%------------------------------------------------------------------------------