%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 02:43:55 PM UTC 2026
% Result : Theorem 9.05s 6.88s
% Output : Proof 9.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 34 unt; 0 def)
% Number of atoms : 191 ( 20 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 208 ( 69 ~; 55 |; 68 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 97 ( 2 sgn 59 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,conjecture,
! [E,P,R] :
( ( ! [A,B] :
( ( member(B,E)
& member(A,E) )
=> ( apply(R,A,B)
<=> ( apply(P,B,A)
& apply(P,A,B) ) ) )
& pre_order(P,E) )
=> ! [X1,X2,Y1,Y2] :
( ( member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
=> ( ( apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1) )
=> apply(P,Y1,Y2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
fof(f16_neg,negated_conjecture,
~ ! [E,P,R] :
( ( ! [A,B] :
( ( member(B,E)
& member(A,E) )
=> ( apply(R,A,B)
<=> ( apply(P,B,A)
& apply(P,A,B) ) ) )
& pre_order(P,E) )
=> ! [X1,X2,Y1,Y2] :
( ( member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
=> ( ( apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1) )
=> apply(P,Y1,Y2) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [E,P,R] :
( ? [X1,X2,Y1,Y2] :
( ~ apply(P,Y1,Y2)
& apply(P,X1,X2)
& apply(R,X2,Y2)
& apply(R,X1,Y1)
& member(Y2,E)
& member(Y1,E)
& member(X2,E)
& member(X1,E) )
& ! [A,B] :
( ( ( ~ apply(P,B,A)
| ~ apply(P,A,B)
| apply(R,A,B) )
& ( ( apply(P,B,A)
& apply(P,A,B) )
| ~ apply(R,A,B) ) )
| ~ member(B,E)
| ~ member(A,E) )
& pre_order(P,E) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
! [A,B] :
( ~ apply(sk21,sk25,sk26)
& apply(sk21,sk23,sk24)
& apply(sk22,sk24,sk26)
& apply(sk22,sk23,sk25)
& member(sk26,sk20)
& member(sk25,sk20)
& member(sk24,sk20)
& member(sk23,sk20)
& ( ( ( ~ apply(sk21,B,A)
| ~ apply(sk21,A,B)
| apply(sk22,A,B) )
& ( ( apply(sk21,B,A)
& apply(sk21,A,B) )
| ~ apply(sk22,A,B) ) )
| ~ member(B,sk20)
| ~ member(A,sk20) )
& pre_order(sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f16_nnf]) ).
cnf(c125,plain,
( apply(sk21,X3,X4)
| ~ apply(sk22,X3,X4)
| ~ member(X4,sk20)
| ~ member(X3,sk20) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi122,negated_conjecture,
ifeq(member(X0,sk20),true,ifeq(member(X1,sk20),true,ifeq(apply(sk22,X0,X1),true,apply(sk21,X0,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(c129,plain,
member(sk24,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi126,negated_conjecture,
member(sk24,sk20) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(c131,plain,
member(sk26,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi128,negated_conjecture,
member(sk26,sk20) = true,
inference(equality_encoding,[status(esa)],[c131]) ).
cnf(c133,plain,
apply(sk22,sk24,sk26),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi130,negated_conjecture,
apply(sk22,sk24,sk26) = true,
inference(equality_encoding,[status(esa)],[c133]) ).
cnf(h108,plain,
apply(sk21,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi122,hi126,hi128,hi130]) ).
cnf(c126,plain,
( apply(sk21,X4,X3)
| ~ apply(sk22,X3,X4)
| ~ member(X4,sk20)
| ~ member(X3,sk20) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi123,negated_conjecture,
ifeq(member(X0,sk20),true,ifeq(member(X1,sk20),true,ifeq(apply(sk22,X0,X1),true,apply(sk21,X1,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(c128,plain,
member(sk23,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi125,negated_conjecture,
member(sk23,sk20) = true,
inference(equality_encoding,[status(esa)],[c128]) ).
cnf(c130,plain,
member(sk25,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi127,negated_conjecture,
member(sk25,sk20) = true,
inference(equality_encoding,[status(esa)],[c130]) ).
cnf(c132,plain,
apply(sk22,sk23,sk25),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi129,negated_conjecture,
apply(sk22,sk23,sk25) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(h98,plain,
apply(sk21,sk25,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi123,hi125,hi127,hi129]) ).
fof(f15,axiom,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pre_order) ).
fof(f15_nnf,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X] :
( ~ apply(R,X,X)
& member(X,E) )
| pre_order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) )
| ~ pre_order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [R,E,X,Y,Z] :
( ( ( ~ apply(R,sk17(R,E),sk19(R,E))
& apply(R,sk18(R,E),sk19(R,E))
& apply(R,sk17(R,E),sk18(R,E))
& member(sk19(R,E),E)
& member(sk18(R,E),E)
& member(sk17(R,E),E) )
| ( ~ apply(R,sk16(R,E),sk16(R,E))
& member(sk16(R,E),E) )
| pre_order(R,E) )
& ( ( ( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ( apply(R,X,X)
| ~ member(X,E) ) )
| ~ pre_order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18,sk19])],[f15_nnf]) ).
cnf(c111,plain,
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi108,axiom,
ifeq(pre_order(X0,X1),true,ifeq(member(X2,X1),true,ifeq(member(X3,X1),true,ifeq(member(X4,X1),true,ifeq(apply(X0,X2,X3),true,ifeq(apply(X0,X3,X4),true,apply(X0,X2,X4),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c111]) ).
cnf(c124,plain,
pre_order(sk21,sk20),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi121,negated_conjecture,
pre_order(sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(c134,plain,
apply(sk21,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi131,negated_conjecture,
apply(sk21,sk23,sk24) = true,
inference(equality_encoding,[status(esa)],[c134]) ).
cnf(h161,plain,
apply(sk21,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi108,hi121,hi127,hi125,hi126,h98,hi131]) ).
cnf(h221,plain,
apply(sk21,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi108,hi121,hi127,hi126,hi128,h161,h108]) ).
cnf(c135,plain,
~ apply(sk21,sk25,sk26),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi135,negated_conjecture,
ifeq(apply(sk21,sk25,sk26),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c135]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi135,h221]) ).
cnf(t4738,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f5,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f5_nnf,plain,
! [X] : ~ member(X,empty_set),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : ~ member(X,empty_set),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c14,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f6_nnf,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,E,A] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f11,axiom,
! [A,B] :
( disjoint(A,B)
<=> ~ ? [X] :
( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
fof(f11_nnf,plain,
! [A,B] :
( ( ? [X] :
( member(X,B)
& member(X,A) )
| disjoint(A,B) )
& ( ! [X] :
( ~ member(X,B)
| ~ member(X,A) )
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,X] :
( ( ( member(sk3(A,B),B)
& member(sk3(A,B),A) )
| disjoint(A,B) )
& ( ~ member(X,B)
| ~ member(X,A)
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c29,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c29,c135]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4738]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 11:55:29 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.05/6.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.05/6.88 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------