%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU267+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 : n017.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 02:56:25 PM UTC 2026
% Result : Theorem 3.64s 1.18s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 62 ~; 54 |; 14 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 140 !; 18 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f26,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_first(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f36,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_second(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f60,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(f317,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f325,conjecture,
! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f326,negated_conjecture,
~ ! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f325]) ).
fof(f344,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f26]) ).
fof(f345,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f36]) ).
fof(f384,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) ) ),
inference(ennf_transformation,[],[f344]) ).
fof(f389,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) ) ),
inference(ennf_transformation,[],[f345]) ).
fof(f667,plain,
? [X0,X1] :
( pair_second(ordered_pair(X0,X1)) != X1
| pair_first(ordered_pair(X0,X1)) != X0 ),
inference(ennf_transformation,[],[f326]) ).
fof(f724,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_first(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X4 )
| pair_first(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f384]) ).
fof(f725,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X2 )
| pair_first(X0) = X1 ) ) ),
inference(rectify,[],[f724]) ).
fof(f726,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ( ordered_pair(sK20(X0,X1),sK21(X0,X1)) = X0
& sK20(X0,X1) != X1 )
| pair_first(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X2,sK20(X0,X1)),skolemize(X3,sK21(X0,X1))],[f725]) ).
fof(f750,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_second(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X5 )
| pair_second(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f389]) ).
fof(f751,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X3 )
| pair_second(X0) = X1 ) ) ),
inference(rectify,[],[f750]) ).
fof(f752,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ( ordered_pair(sK33(X0,X1),sK34(X0,X1)) = X0
& sK34(X0,X1) != X1 )
| pair_second(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34]),skolemize(X2,sK33(X0,X1)),skolemize(X3,sK34(X0,X1))],[f751]) ).
fof(f945,plain,
( sK133 != pair_second(ordered_pair(sK132,sK133))
| sK132 != pair_first(ordered_pair(sK132,sK133)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132,sK133]),skolemize(X0,sK132),skolemize(X1,sK133)],[f667]) ).
fof(f968,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f1033,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_first(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X4 ),
inference(cnf_transformation,[],[f726]) ).
fof(f1069,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_second(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X5 ),
inference(cnf_transformation,[],[f752]) ).
fof(f1178,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f60]) ).
fof(f1611,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f317]) ).
fof(f1622,plain,
( sK133 != pair_second(ordered_pair(sK132,sK133))
| sK132 != pair_first(ordered_pair(sK132,sK133)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1651,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1178,f1611]) ).
fof(f1681,plain,
! [X0,X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| pair_first(X0) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| X1 = X4 ),
inference(definition_unfolding,[],[f1033,f1651,f1651]) ).
fof(f1696,plain,
! [X0,X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| pair_second(X0) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| X1 = X5 ),
inference(definition_unfolding,[],[f1069,f1651,f1651]) ).
fof(f1839,plain,
( sK133 != pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132)))
| sK132 != pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) ),
inference(definition_unfolding,[],[f1622,f1651,f1651]) ).
fof(f1881,plain,
! [X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| X1 = X4 ),
inference(equality_resolution,[],[f1681]) ).
fof(f1882,plain,
! [X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X4 ),
inference(equality_resolution,[],[f1881]) ).
fof(f1902,plain,
! [X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| X1 = X5 ),
inference(equality_resolution,[],[f1696]) ).
fof(f1903,plain,
! [X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X5 ),
inference(equality_resolution,[],[f1902]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f968]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f1882]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f1903]) ).
tcf(c_711,negated_conjecture,
( ( pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK133 )
| ( pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK132 ) ),
inference(cnf_transformation,[],[f1839]) ).
tcf(c_907,plain,
( ( pair_second(unordered_pair(unordered_pair(sK132,sK132),unordered_pair(sK132,sK133))) != sK133 )
| ( pair_first(unordered_pair(unordered_pair(sK132,sK132),unordered_pair(sK132,sK133))) != sK132 ) ),
inference(demodulation,[status(thm)],[c_711,c_61]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(equality_resolution,[status(thm)],[c_163]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(equality_resolution,[status(thm)],[c_128]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1))) = X1,
inference(superposition,[status(thm)],[c_61,c_924]) ).
tcf(c_1082,plain,
pair_first(unordered_pair(unordered_pair(sK132,sK132),unordered_pair(sK132,sK133))) != sK132,
inference(backward_subsumption_resolution,[status(thm)],[c_907,c_1078]) ).
tcf(c_1100,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_61,c_938]) ).
tcf(c_1240,plain,
$false,
inference(superposition,[status(thm)],[c_1100,c_1082]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:23:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 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...
% 3.64/1.18 % SZS status Started for theBenchmark.p
% 3.64/1.18 % SZS status Theorem for theBenchmark.p
% 3.64/1.18
% 3.64/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.64/1.18
% 3.64/1.18 % ------ iProver source info
% 3.64/1.18
% 3.64/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.64/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.64/1.18 % git: non_committed_changes: false
% 3.64/1.18
% 3.64/1.18 % ------ Parsing...
% 3.64/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.64/1.18 % ------ Proving...
% 3.64/1.18 % ------ Problem Properties
% 3.64/1.18
% 3.64/1.18 %
% 3.64/1.18 % clauses 690
% 3.64/1.18 % conjectures 1
% 3.64/1.18 % EPR 120
% 3.64/1.18 % Horn 552
% 3.64/1.18 % unary 104
% 3.64/1.18 % binary 177
% 3.64/1.18 % lits 2048
% 3.64/1.18 % lits eq 312
% 3.64/1.18 % fd_pure 0
% 3.64/1.18 % fd_pseudo 0
% 3.64/1.18 % fd_cond 21
% 3.64/1.18 % fd_pseudo_cond 105
% 3.64/1.18 % AC symbols 0
% 3.64/1.18
% 3.64/1.18 % ------ Input Options Time Limit: Unbounded
% 3.64/1.18
% 3.64/1.18
% 3.64/1.18 % ------
% 3.64/1.18 % Current options:
% 3.64/1.18 % ------
% 3.64/1.18
% 3.64/1.18
% 3.64/1.18 %
% 3.64/1.18
% 3.64/1.18 % ------ Proving...
% 3.64/1.18 %
% 3.64/1.18
% 3.64/1.18 % SZS status Theorem for theBenchmark.p
% 3.64/1.18
% 3.64/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.64/1.18
%------------------------------------------------------------------------------