%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:44:14 PM UTC 2026
% Result : Theorem 3.99s 1.08s
% Output : Proof 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 54 unt; 0 def)
% Number of atoms : 70 ( 56 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 63 ( 8 sgn 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B,C] :
( unordered_pair(A,B) != singleton(C)
& subset(unordered_pair(A,B),singleton(C)) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( unordered_pair(sk2,sk3) != singleton(sk4)
& subset(unordered_pair(sk2,sk3),singleton(sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f5_nnf]) ).
cnf(c6,plain,
unordered_pair(sk2,sk3) != singleton(sk4),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t8,plain,
ifeq(unordered_pair(sk2,sk3),singleton(sk4),false,true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t12,plain,
ifeq(unordered_pair(sk2,sk3),singleton(sk4),false,true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t20,plain,
ifeq(unordered_pair(sk2,sk3),singleton(sk4),false,true) = true,
inference(rw,[status(thm)],[t12]) ).
fof(f0,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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(t18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t37,plain,
ifeq(unordered_pair(sk3,sk2),singleton(sk4),false,true) = true,
inference(step,[status(thm)],[t20,t18]) ).
fof(f4,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B,C] :
( A = C
| ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( A = C
| ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X0 = X2
| ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(subset(unordered_pair(X0,X1),singleton(X2)),true,X0,X2) = X2,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c5,plain,
subset(unordered_pair(sk2,sk3),singleton(sk4)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
subset(unordered_pair(sk2,sk3),singleton(sk4)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f6,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f6_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t0,plain,
sk4 = sk2,
inference(hyper_resolution,[status(thm)],[hi3,hi5,hi4]) ).
cnf(t24,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t0]) ).
cnf(t38,plain,
ifeq(unordered_pair(sk3,sk4),singleton(sk4),false,true) = true,
inference(step,[status(thm)],[t37,t24]) ).
cnf(t39,plain,
ifeq(unordered_pair(sk4,sk3),singleton(sk4),false,true) = true,
inference(step,[status(thm)],[t38,t18]) ).
cnf(t26,plain,
ifeq(unordered_pair(sk4,sk3),singleton(sk4),false,true) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t9,plain,
ifeq(subset(unordered_pair(X1,X2),singleton(X3)),true,X1,X3) = X3,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t11,plain,
ifeq(subset(unordered_pair(X1,X2),singleton(X3)),true,X1,X3) = X3,
inference(orient,[status(thm)],[t9]) ).
cnf(t19,plain,
X1 = ifeq(subset(unordered_pair(X2,X3),singleton(X1)),true,X3,X1),
inference(cp,[status(thm)],[t11,t18]) ).
cnf(t28,plain,
ifeq(subset(unordered_pair(X1,X2),singleton(X3)),true,X2,X3) = X3,
inference(orient,[status(thm)],[t19]) ).
cnf(t7,plain,
subset(unordered_pair(sk2,sk3),singleton(sk4)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t15,plain,
subset(unordered_pair(sk2,sk3),singleton(sk4)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t21,plain,
subset(unordered_pair(sk2,sk3),singleton(sk4)) = true,
inference(rw,[status(thm)],[t15]) ).
cnf(t34,plain,
subset(unordered_pair(sk3,sk2),singleton(sk4)) = true,
inference(step,[status(thm)],[t21,t18]) ).
cnf(t35,plain,
subset(unordered_pair(sk3,sk4),singleton(sk4)) = true,
inference(step,[status(thm)],[t34,t24]) ).
cnf(t36,plain,
subset(unordered_pair(sk4,sk3),singleton(sk4)) = true,
inference(step,[status(thm)],[t35,t18]) ).
cnf(t25,plain,
subset(unordered_pair(sk4,sk3),singleton(sk4)) = true,
inference(orient,[status(thm)],[t36]) ).
cnf(t29,plain,
sk4 = ifeq(true,true,sk3,sk4),
inference(cp,[status(thm)],[t28,t25]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t40,plain,
sk4 = sk3,
inference(step,[status(thm)],[t29,t10]) ).
cnf(t30,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t40]) ).
cnf(t41,plain,
ifeq(unordered_pair(sk4,sk4),singleton(sk4),false,true) = true,
inference(step,[status(thm)],[t26,t30]) ).
cnf(t3,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t22,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t42,plain,
ifeq(singleton(sk4),singleton(sk4),false,true) = true,
inference(step,[status(thm)],[t41,t22]) ).
cnf(t43,plain,
false = true,
inference(step,[status(thm)],[t42,t10]) ).
cnf(t31,plain,
false = true,
inference(rw,[status(thm)],[t43]) ).
cnf(t32,plain,
false = true,
inference(orient,[status(thm)],[t31]) ).
fof(f2,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t32]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:23:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.99/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------