%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 08:45:38 AM UTC 2026
% Result : Theorem 3.12s 0.96s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 29 unt; 0 def)
% Number of atoms : 168 ( 135 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 183 ( 73 ~; 73 |; 26 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 183 ( 40 sgn 73 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('theBenchmark.p',d1_mcart_1) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('theBenchmark.p',d2_mcart_1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(d1_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(t7_mcart_1,conjecture,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
fof(t7_mcart_1_neg,negated_conjecture,
~ ! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(assume_negation,[status(cth)],[t7_mcart_1]) ).
fof(nnf_287,plain,
! [A,B,C,D] :
( ( ? [E] :
( ( ( E != C
& E != B
& E != A )
| ~ in(E,D) )
& ( E = C
| E = B
| E = A
| in(E,D) ) )
| unordered_triple(A,B,C) = D )
& ( ! [X0] :
( ( ( X0 != C
& X0 != B
& X0 != A )
| in(X0,D) )
& ( X0 = C
| X0 = B
| X0 = A
| ~ in(X0,D) ) )
| unordered_triple(A,B,C) != D ) ),
inference(fof_nnf,[status(thm)],[d1_enumset1]) ).
fof(sk_d1_enumset1_sk,plain,
! [A,B,C,D] :
( ( ( ( ( sK0(A,B,C,D) != C
& sK0(A,B,C,D) != B
& sK0(A,B,C,D) != A )
| ~ in(sK0(A,B,C,D),D) )
& ( sK0(A,B,C,D) = C
| sK0(A,B,C,D) = B
| sK0(A,B,C,D) = A
| in(sK0(A,B,C,D),D) ) )
| unordered_triple(A,B,C) = D )
& ( ! [X0] :
( ( ( X0 != C
& X0 != B
& X0 != A )
| in(X0,D) )
& ( X0 = C
| X0 = B
| X0 = A
| ~ in(X0,D) ) )
| unordered_triple(A,B,C) != D ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(E,sK0(A,B,C,D))],[nnf_287]) ).
fof(sk_d1_enumset1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK0(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_2
| ~ in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) = VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK0(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_1
| ~ in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) = VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK0(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_0
| ~ in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) = VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK0(VAR_0,VAR_1,VAR_2,VAR_3) = VAR_2
| sK0(VAR_0,VAR_1,VAR_2,VAR_3) = VAR_1
| sK0(VAR_0,VAR_1,VAR_2,VAR_3) = VAR_0
| in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) = VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( VAR_4 != VAR_2
| in(VAR_4,VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) != VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( VAR_4 != VAR_1
| in(VAR_4,VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) != VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( VAR_4 != VAR_0
| in(VAR_4,VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) != VAR_3 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( VAR_4 = VAR_2
| VAR_4 = VAR_1
| VAR_4 = VAR_0
| ~ in(VAR_4,VAR_3)
| unordered_triple(VAR_0,VAR_1,VAR_2) != VAR_3 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_enumset1_sk]) ).
cnf(c_346,plain,
( E != C
| in(E,D)
| unordered_triple(A,B,C) != D ),
inference(split_conjunct,[status(thm)],[sk_d1_enumset1]) ).
cnf(c_347,plain,
( sK0(A,B,C,D) = C
| sK0(A,B,C,D) = B
| sK0(A,B,C,D) = A
| in(sK0(A,B,C,D),D)
| unordered_triple(A,B,C) = D ),
inference(split_conjunct,[status(thm)],[sk_d1_enumset1]) ).
cnf(c_488,plain,
( E = D
| ordered_pair(E,F) != C
| pair_first(C) != D
| ordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d1_mcart_1]) ).
cnf(c_519,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_525,plain,
( F = D
| ordered_pair(E,F) != C
| pair_second(C) != D
| ordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_mcart_1]) ).
cnf(c_612,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_906,plain,
set_intersection2(A,empty_set) = empty_set,
inference(clausify,[status(thm)],[t2_boole]) ).
cnf(c_937,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_958,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_959,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_958]) ).
fof(nnf_340,plain,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
| pair_first(ordered_pair(A,B)) != A ),
inference(fof_nnf,[status(thm)],[t7_mcart_1_neg]) ).
fof(sk_t7_mcart_1_neg,plain,
( pair_second(ordered_pair(sK1,sK2)) != sK2
| pair_first(ordered_pair(sK1,sK2)) != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_340]) ).
cnf(c_1040,negated_conjecture,
( pair_second(ordered_pair(sK1,sK2)) != sK2
| pair_first(ordered_pair(sK1,sK2)) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t7_mcart_1_neg]) ).
cnf(c_1060,plain,
( A = D
| pair_first(C) != D
| ordered_pair(A,B) != C ),
inference(factor,[status(thm)],[c_488]) ).
cnf(c_1070,plain,
( B = D
| pair_second(C) != D
| ordered_pair(A,B) != C ),
inference(factor,[status(thm)],[c_525]) ).
cnf(c_1089,plain,
( ~ in(C,B)
| set_difference(A,B) != B ),
inference(factor,[status(thm)],[c_612]) ).
cnf(c_2796,plain,
set_difference(A,set_difference(A,empty_set)) = empty_set,
inference(paramod,[status(thm)],[c_959,c_906]) ).
cnf(c_1182,plain,
set_difference(A,A) = empty_set,
inference(paramod,[status(thm)],[c_937,c_2796]) ).
cnf(c_2797,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_1089,c_1182]) ).
cnf(c_1303,plain,
( sK0(A,B,C,empty_set) = C
| sK0(A,B,C,empty_set) = B
| sK0(A,B,C,empty_set) = A
| unordered_triple(A,B,C) = empty_set ),
inference(resolve,[status(thm)],[c_2797,c_347]) ).
cnf(c_1310,plain,
( sK0(A,A,B,empty_set) = B
| sK0(A,A,B,empty_set) = A
| unordered_triple(A,A,B) = empty_set ),
inference(factor,[status(thm)],[c_1303]) ).
cnf(c_1313,plain,
( sK0(A,A,A,empty_set) = A
| unordered_triple(A,A,A) = empty_set ),
inference(factor,[status(thm)],[c_1310]) ).
cnf(c_2798,plain,
( A = C
| pair_first(ordered_pair(A,B)) != C ),
inference(xxres,[status(thm)],[c_1060]) ).
cnf(c_2799,plain,
A = pair_first(ordered_pair(A,B)),
inference(xxres,[status(thm)],[c_2798]) ).
cnf(c_1872,plain,
pair_first(ordered_pair(A,B)) = A,
inference(copy,[status(thm)],[c_2799]) ).
cnf(c_2800,negated_conjecture,
( pair_second(ordered_pair(sK1,sK2)) != sK2
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_1872,c_1040]) ).
cnf(c_1873,negated_conjecture,
pair_second(ordered_pair(sK1,sK2)) != sK2,
inference(copy,[status(thm)],[c_2800]) ).
cnf(c_2801,plain,
A = pair_first(ordered_pair(A,B)),
inference(copy,[status(thm)],[c_1872]) ).
cnf(c_2802,plain,
( A != D
| in(A,pair_first(ordered_pair(unordered_triple(B,C,D),E))) ),
inference(resolve,[status(thm)],[c_346,c_2801]) ).
cnf(c_2803,plain,
in(pair_first(ordered_pair(A,B)),pair_first(ordered_pair(unordered_triple(C,D,A),E))),
inference(resolve,[status(thm)],[c_2802,c_1872]) ).
cnf(c_2804,plain,
in(A,pair_first(ordered_pair(unordered_triple(C,D,A),E))),
inference(paramod,[status(thm)],[c_1872,c_2803]) ).
cnf(c_1886,plain,
in(A,unordered_triple(B,C,A)),
inference(paramod,[status(thm)],[c_1872,c_2804]) ).
cnf(c_2805,plain,
empty_set != unordered_triple(A,B,C),
inference(resolve,[status(thm)],[c_1886,c_519]) ).
cnf(c_2347,plain,
unordered_triple(A,B,C) != empty_set,
inference(copy,[status(thm)],[c_2805]) ).
cnf(c_2366,plain,
sK0(A,A,A,empty_set) = A,
inference(resolve,[status(thm)],[c_2347,c_1313]) ).
cnf(c_2806,plain,
A = sK0(A,A,A,empty_set),
inference(copy,[status(thm)],[c_2366]) ).
cnf(c_2807,plain,
( B = C
| pair_second(sK0(ordered_pair(A,B),ordered_pair(A,B),ordered_pair(A,B),empty_set)) != C ),
inference(resolve,[status(thm)],[c_1070,c_2806]) ).
cnf(c_2808,plain,
A = sK0(A,A,A,empty_set),
inference(copy,[status(thm)],[c_2366]) ).
cnf(c_2809,plain,
A = sK0(pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),empty_set),
inference(resolve,[status(thm)],[c_2807,c_2808]) ).
cnf(c_2810,plain,
A = sK0(pair_second(ordered_pair(B,A)),pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),empty_set),
inference(paramod,[status(thm)],[c_2366,c_2809]) ).
cnf(c_2811,plain,
A = sK0(pair_second(ordered_pair(B,A)),pair_second(ordered_pair(B,A)),pair_second(sK0(ordered_pair(B,A),ordered_pair(B,A),ordered_pair(B,A),empty_set)),empty_set),
inference(paramod,[status(thm)],[c_2366,c_2810]) ).
cnf(c_2812,plain,
A = sK0(pair_second(ordered_pair(B,A)),pair_second(ordered_pair(B,A)),pair_second(ordered_pair(B,A)),empty_set),
inference(paramod,[status(thm)],[c_2366,c_2811]) ).
cnf(c_2813,plain,
A = pair_second(ordered_pair(B,A)),
inference(paramod,[status(thm)],[c_2366,c_2812]) ).
cnf(c_2794,plain,
pair_second(ordered_pair(A,B)) = B,
inference(copy,[status(thm)],[c_2813]) ).
cnf(c_2795,plain,
$false,
inference(resolve,[status(thm)],[c_2794,c_1873]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 09:01:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1778045 was started by sandbox2 on n005,
% 0.18/0.44 % Sat Sep 26 09:01:32 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.24/0.52
% 0.24/0.52 % From the command line: assign(max_seconds, 300).
% 0.24/0.52
% 0.24/0.52 % SInE: 286 to sos, 55 to usable, of 341 axioms (tolerance 2.00, depth 0 fixpoint).
% 3.12/0.96
% 3.12/0.96 % SZS status Theorem for theBenchmark
% 3.12/0.96
% 3.12/0.96 % Proof 1 at 0.33 (+ 0.07) seconds.
% 3.12/0.96 % Length of proof is 34.
% 3.12/0.96 % Level of proof is 9.
% 3.12/0.96 % Maximum clause weight is 229.000.
% 3.12/0.96 % Given clauses 275.
% 3.12/0.96
% 3.12/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------