%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU155+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 : n026.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 02:51:08 PM UTC 2026
% Result : Theorem 5.33s 1.16s
% Output : Proof 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 34 unt; 0 def)
% Number of atoms : 105 ( 37 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 91 ( 37 ~; 28 |; 19 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 81 ( 2 sgn 31 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c3,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t16,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t50,plain,
ifeq(in(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t16]) ).
fof(f2,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
& ~ in(C,B) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C,D] :
( ( ( in(sk3(A,B),A)
& in(sk2(A,B),sk3(A,B))
& ~ in(sk2(A,B),B) )
| ( ( ~ in(D,A)
| ~ in(sk2(A,B),D) )
& in(sk2(A,B),B) )
| B = union(A) )
& ( ( ( ~ in(D,A)
| ~ in(C,D)
| in(C,B) )
& ( ( in(sk1(A,B,C),A)
& in(C,sk1(A,B,C)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f2_nnf]) ).
cnf(c6,plain,
( ~ in(X3,X0)
| ~ in(X2,X3)
| in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t23,plain,
ifeq(X1,union(X2),ifeq(in(X3,X4),true,ifeq(in(X4,X2),true,in(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
ifeq(X1,union(X2),ifeq(in(X3,X4),true,ifeq(in(X4,X2),true,in(X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t33,plain,
true = ifeq(in(X1,X2),true,ifeq(in(X2,X3),true,in(X1,union(X3)),true),true),
inference(cp,[status(thm)],[t32,t27]) ).
cnf(t150,plain,
ifeq(in(X1,X2),true,ifeq(in(X2,X3),true,in(X1,union(X3)),true),true) = true,
inference(orient,[status(thm)],[t33]) ).
fof(f4,conjecture,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B] :
( ~ subset(A,union(B))
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ~ subset(sk4,union(sk5))
& in(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f4_nnf]) ).
cnf(c14,plain,
in(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t3,plain,
in(sk4,sk5) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t31,plain,
in(sk4,sk5) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t156,plain,
true = ifeq(in(X1,sk4),true,ifeq(true,true,in(X1,union(sk5)),true),true),
inference(cp,[status(thm)],[t150,t31]) ).
cnf(t221,plain,
true = ifeq(in(X1,sk4),true,in(X1,union(sk5)),true),
inference(step,[status(thm)],[t156,t27]) ).
cnf(t162,plain,
ifeq(in(X1,sk4),true,in(X1,union(sk5)),true) = true,
inference(orient,[status(thm)],[t221]) ).
cnf(c2,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t15,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t57,plain,
or(subset(X1,X2),in(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(c15,plain,
~ subset(sk4,union(sk5)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
subset(sk4,union(sk5)) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t73,plain,
subset(sk4,union(sk5)) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t74,plain,
true = or(false,in(sk0(sk4,union(sk5)),sk4)),
inference(cp,[status(thm)],[t57,t73]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t30,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t207,plain,
true = in(sk0(sk4,union(sk5)),sk4),
inference(step,[status(thm)],[t74,t30]) ).
cnf(t82,plain,
in(sk0(sk4,union(sk5)),sk4) = true,
inference(orient,[status(thm)],[t207]) ).
cnf(t164,plain,
true = ifeq(true,true,in(sk0(sk4,union(sk5)),union(sk5)),true),
inference(cp,[status(thm)],[t162,t82]) ).
cnf(t223,plain,
true = in(sk0(sk4,union(sk5)),union(sk5)),
inference(step,[status(thm)],[t164,t27]) ).
cnf(t168,plain,
in(sk0(sk4,union(sk5)),union(sk5)) = true,
inference(orient,[status(thm)],[t223]) ).
cnf(t175,plain,
true = ifeq(true,true,subset(sk4,union(sk5)),true),
inference(cp,[status(thm)],[t50,t168]) ).
cnf(t226,plain,
true = subset(sk4,union(sk5)),
inference(step,[status(thm)],[t175,t27]) ).
cnf(t227,plain,
true = false,
inference(step,[status(thm)],[t226,t73]) ).
cnf(t188,plain,
false = true,
inference(orient,[status(thm)],[t227]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t188]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU155+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 13:01:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.33/1.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.33/1.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------