%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 02:44:16 PM UTC 2026
% Result : Theorem 10.18s 7.00s
% Output : Proof 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 37 unt; 0 def)
% Number of atoms : 130 ( 70 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 44 |; 26 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 110 ( 12 sgn 59 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D = B
| D = A )
& ~ in(D,C) )
| ( D != B
& D != A
& in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( ( sk1(A,B,C) = B
| sk1(A,B,C) = A )
& ~ in(sk1(A,B,C),C) )
| ( sk1(A,B,C) != B
& sk1(A,B,C) != A
& in(sk1(A,B,C),C) )
| C = unordered_pair(A,B) )
& ( ( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c7,plain,
( X3 != X1
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,axiom,
ifeq(X0,unordered_pair(X1,X2),ifeq(X3,X2,in(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f9,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f9_nnf,plain,
! [A,B] : set_union2(A,A) = A,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : set_union2(A,A) = A,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c26,plain,
set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi18,axiom,
set_union2(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h138,plain,
in(set_union2(V0,V0),unordered_pair(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi0,hi18]) ).
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
| in(D,A) )
& ~ in(D,C) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk2(A,B,C),B)
| in(sk2(A,B,C),A) )
& ~ in(sk2(A,B,C),C) )
| ( ~ in(sk2(A,B,C),B)
& ~ in(sk2(A,B,C),A)
& in(sk2(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c15,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi10,axiom,
ifeq(X0,set_union2(X1,X2),ifeq(in(X3,X1),true,in(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f12,conjecture,
! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f12_neg,negated_conjecture,
~ ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [A,B,C] : set_union2(unordered_pair(A,B),C) = empty_set,
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
set_union2(unordered_pair(sk5,sk6),sk7) = empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f12_nnf]) ).
cnf(c29,plain,
set_union2(unordered_pair(sk5,sk6),sk7) = empty_set,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi20,negated_conjecture,
set_union2(unordered_pair(sk5,sk6),sk7) = empty_set,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h734,plain,
in(set_union2(sk5,sk5),empty_set) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi20,h138]) ).
cnf(c16,plain,
( ~ in(X3,X1)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi11,axiom,
ifeq(X0,set_union2(X1,X2),ifeq(in(X3,X2),true,in(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
set_union2(X0,X1) = set_union2(X1,X0),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h755,plain,
in(set_union2(sk5,sk5),set_union2(empty_set,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi1,h734]) ).
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c3,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi22,axiom,
ifeq(X0,empty_set,ifeq(in(X1,X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi22,hi18,h755]) ).
cnf(t526,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f11,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f11_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ empty(sk4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f11_nnf]) ).
cnf(c28,plain,
~ empty(sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c3,c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t526]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n017.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 12:17:08 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.18/7.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.18/7.00 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------