%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU150+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 0.16s 6.05s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 43 unt; 0 def)
% Number of atoms : 59 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 55 ( 6 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f2_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c2,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t6,plain,
ifeq(empty(sk1),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t11,plain,
ifeq(empty(sk1),true,false,true) = true,
inference(orient,[status(thm)],[t6]) ).
fof(f1,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f1_nnf,plain,
? [A] : empty(A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
empty(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c1,plain,
empty(sk0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
empty(sk0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
empty(sk0) = true,
inference(orient,[status(thm)],[t1]) ).
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(t7,plain,
ifeq(singleton(X1),unordered_pair(X2,X3),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
ifeq(singleton(X1),unordered_pair(X2,X3),X1,X2) = X2,
inference(orient,[status(thm)],[t7]) ).
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,
( sk3 != sk4
& singleton(sk2) = unordered_pair(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c4,plain,
singleton(sk2) = unordered_pair(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t2,plain,
unordered_pair(sk3,sk4) = singleton(sk2),
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(t5,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t28,plain,
unordered_pair(sk4,sk3) = singleton(sk2),
inference(step,[status(thm)],[t2,t13]) ).
cnf(t15,plain,
unordered_pair(sk4,sk3) = singleton(sk2),
inference(orient,[status(thm)],[t28]) ).
cnf(t16,plain,
sk4 = ifeq(singleton(X1),singleton(sk2),X1,sk4),
inference(cp,[status(thm)],[t9,t15]) ).
cnf(hi2,axiom,
ifeq(singleton(X0),unordered_pair(X1,X2),X0,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi3,negated_conjecture,
singleton(sk2) = unordered_pair(sk3,sk4),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t0,plain,
sk3 = sk2,
inference(hyper_resolution,[status(thm)],[hi2,hi3]) ).
cnf(t17,plain,
sk2 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,plain,
sk4 = ifeq(singleton(X1),singleton(sk3),X1,sk4),
inference(step,[status(thm)],[t16,t17]) ).
cnf(t20,plain,
ifeq(singleton(X1),singleton(sk3),X1,sk4) = sk4,
inference(orient,[status(thm)],[t31]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t21,plain,
sk4 = sk3,
inference(cp,[status(thm)],[t20,t8]) ).
cnf(t22,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t21]) ).
cnf(c5,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c5]) ).
cnf(g0_0,plain,
true != ifeq(sk3,sk4,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(sk3,sk4,false,ifeq(empty(sk1),true,false,true)),
inference(rw,[status(thm)],[g0_0,t11]) ).
cnf(g0_2,plain,
true != ifeq(sk3,sk4,false,ifeq(empty(sk1),true,false,empty(sk0))),
inference(rw,[status(thm)],[g0_1,t12]) ).
cnf(g0_3,plain,
true != ifeq(sk3,sk3,false,ifeq(empty(sk1),true,false,empty(sk0))),
inference(rw,[status(thm)],[g0_2,t22]) ).
cnf(g0_4,plain,
true != false,
inference(rw,[status(thm)],[g0_3,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n003.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 12:59:27 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/6.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/6.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------