%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU150+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 02:51:06 PM UTC 2026
% Result : Theorem 0.13s 5.85s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 27 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 51 ( 6 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t4,plain,
ifeq(singleton(X1),unordered_pair(X2,X3),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t6,plain,
ifeq(singleton(X1),unordered_pair(X2,X3),X1,X2) = X2,
inference(orient,[status(thm)],[t4]) ).
fof(f4,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B,C] :
( B != C
& singleton(A) = unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( sk1 != sk2
& singleton(sk0) = unordered_pair(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f4_nnf]) ).
cnf(c4,plain,
singleton(sk0) = unordered_pair(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t1,plain,
unordered_pair(sk1,sk2) = singleton(sk0),
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f0,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f0_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t21,plain,
unordered_pair(sk2,sk1) = singleton(sk0),
inference(step,[status(thm)],[t1,t7]) ).
cnf(t9,plain,
unordered_pair(sk2,sk1) = singleton(sk0),
inference(orient,[status(thm)],[t21]) ).
cnf(t10,plain,
sk2 = ifeq(singleton(X1),singleton(sk0),X1,sk2),
inference(cp,[status(thm)],[t6,t9]) ).
cnf(hi1,axiom,
ifeq(singleton(X0),unordered_pair(X1,X2),X0,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi2,negated_conjecture,
singleton(sk0) = unordered_pair(sk1,sk2),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t0,plain,
sk1 = sk0,
inference(hyper_resolution,[status(thm)],[hi1,hi2]) ).
cnf(t11,plain,
sk0 = sk1,
inference(orient,[status(thm)],[t0]) ).
cnf(t24,plain,
sk2 = ifeq(singleton(X1),singleton(sk1),X1,sk2),
inference(step,[status(thm)],[t10,t11]) ).
cnf(t14,plain,
ifeq(singleton(X1),singleton(sk1),X1,sk2) = sk2,
inference(orient,[status(thm)],[t24]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t15,plain,
sk2 = sk1,
inference(cp,[status(thm)],[t14,t5]) ).
cnf(t16,plain,
sk1 = sk2,
inference(orient,[status(thm)],[t15]) ).
cnf(c5,plain,
sk1 != sk2,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
sk2 != sk1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
sk2 != sk2,
inference(rw,[status(thm)],[goal_0,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n007.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Thu Sep 24 12:55:44 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/5.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------