%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET081-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:42:03 PM UTC 2026
% Result : Unsatisfiable 9.53s 1.74s
% Output : Proof 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 60 unt; 0 def)
% Number of atoms : 88 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 27 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-4 aty)
% Number of variables : 62 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t92,axiom,
sF1 = ifeq(y,x,false,true),
introduced(definition) ).
cnf(t91,axiom,
sF0 = eq(y,x),
introduced(definition) ).
cnf(f92,negated_conjecture,
y != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_only_member_in_singleton_2) ).
fof(f92_nnf,plain,
y != x,
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
y != x,
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c92,plain,
y != x,
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
cnf(t5,plain,
eq(y,x) = false,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t100,plain,
eq(y,x) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t2690,plain,
sF0 = false,
inference(step,[status(thm)],[t91,t100]) ).
cnf(t107,plain,
false = sF0,
inference(orient,[status(thm)],[t2690]) ).
cnf(t2700,plain,
sF1 = ifeq(y,x,sF0,true),
inference(step,[status(thm)],[t92,t107]) ).
cnf(t13,plain,
ifeq(y,x,false,true) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t2698,plain,
ifeq(y,x,sF0,true) = true,
inference(step,[status(thm)],[t13,t107]) ).
cnf(t120,plain,
ifeq(y,x,sF0,true) = true,
inference(orient,[status(thm)],[t2698]) ).
cnf(t2701,plain,
sF1 = true,
inference(step,[status(thm)],[t2700,t120]) ).
cnf(t127,plain,
true = sF1,
inference(orient,[status(thm)],[t2701]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t56,plain,
ifeq(member(X1,unordered_pair(X2,X3)),true,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t2957,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),true) = true,
inference(step,[status(thm)],[t56,t127]) ).
cnf(t2958,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = true,
inference(step,[status(thm)],[t2957,t127]) ).
cnf(t2959,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = sF1,
inference(step,[status(thm)],[t2958,t127]) ).
cnf(t689,plain,
ifeq(member(X1,unordered_pair(X2,X3)),sF1,or(eq(X1,X2),eq(X1,X3)),sF1) = sF1,
inference(orient,[status(thm)],[t2959]) ).
cnf(t2694,plain,
eq(y,x) = sF0,
inference(step,[status(thm)],[t100,t107]) ).
cnf(t111,plain,
eq(y,x) = sF0,
inference(orient,[status(thm)],[t2694]) ).
cnf(t692,plain,
sF1 = ifeq(member(y,unordered_pair(x,X1)),sF1,or(sF0,eq(y,X1)),sF1),
inference(cp,[status(thm)],[t689,t111]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t104,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t2697,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t104,t107]) ).
cnf(t114,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t2697]) ).
cnf(t118,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t114]) ).
cnf(t3272,plain,
sF1 = ifeq(member(y,unordered_pair(x,X1)),sF1,eq(y,X1),sF1),
inference(step,[status(thm)],[t692,t118]) ).
cnf(t2321,plain,
ifeq(member(y,unordered_pair(x,X1)),sF1,eq(y,X1),sF1) = sF1,
inference(orient,[status(thm)],[t3272]) ).
cnf(t2322,plain,
sF1 = ifeq(member(y,unordered_pair(x,x)),sF1,sF0,sF1),
inference(cp,[status(thm)],[t2321,t111]) ).
cnf(t93,axiom,
sF2 = unordered_pair(x,x),
introduced(definition) ).
cnf(t116,plain,
unordered_pair(x,x) = sF2,
inference(orient,[status(thm)],[t93]) ).
cnf(t3273,plain,
sF1 = ifeq(member(y,sF2),sF1,sF0,sF1),
inference(step,[status(thm)],[t2322,t116]) ).
cnf(f91,negated_conjecture,
member(y,singleton(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_only_member_in_singleton_1) ).
fof(f91_nnf,plain,
member(y,singleton(x)),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
member(y,singleton(x)),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(u8,axiom,
member(y,singleton(x)) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(d0,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t15,plain,
member(y,unordered_pair(x,x)) = true,
inference(definition_unfolding,[status(thm)],[u8,d0]) ).
cnf(t2699,plain,
member(y,sF2) = true,
inference(step,[status(thm)],[t15,t116]) ).
cnf(t124,plain,
member(y,sF2) = true,
inference(orient,[status(thm)],[t2699]) ).
cnf(t2719,plain,
member(y,sF2) = sF1,
inference(step,[status(thm)],[t124,t127]) ).
cnf(t148,plain,
member(y,sF2) = sF1,
inference(orient,[status(thm)],[t2719]) ).
cnf(t3274,plain,
sF1 = ifeq(sF1,sF1,sF0,sF1),
inference(step,[status(thm)],[t3273,t148]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t119,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t3275,plain,
sF1 = sF0,
inference(step,[status(thm)],[t3274,t119]) ).
cnf(t2323,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t3275]) ).
cnf(t3298,plain,
true = sF0,
inference(step,[status(thm)],[t127,t2323]) ).
cnf(t2346,plain,
true = sF0,
inference(orient,[status(thm)],[t3298]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c92]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t2346]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t107]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET081-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.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 09:39:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.53/1.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.53/1.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------