%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET027-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:41:36 PM UTC 2026
% Result : Unsatisfiable 48.79s 6.68s
% Output : Proof 48.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 52 unt; 0 def)
% Number of atoms : 108 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 50 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 88 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f68,axiom,
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset3) ).
fof(f68_nnf,plain,
! [X,Y] :
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [X,Y] :
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t90,plain,
ifeq(member(f17(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t522,plain,
ifeq(member(f17(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(f66,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subset(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset1) ).
fof(f66_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subset(X,Y) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t197,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t609,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t197]) ).
cnf(f142,hypothesis,
subset(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_subset_c) ).
fof(f142_nnf,plain,
subset(b,c),
inference(nnf_transformation,[status(thm)],[f142]) ).
cnf(c142,plain,
subset(b,c),
inference(cnf_transformation,[status(esa)],[f142_nnf]) ).
cnf(t15,plain,
subset(b,c) = true,
inference(equality_encoding,[status(esa)],[c142]) ).
cnf(t1979,plain,
subset(b,c) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t1982,plain,
true = ifeq(true,true,ifeq(member(X1,b),true,member(X1,c),true),true),
inference(cp,[status(thm)],[t609,t1979]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t39216,plain,
true = ifeq(member(X1,b),true,member(X1,c),true),
inference(step,[status(thm)],[t1982,t256]) ).
cnf(t37202,plain,
ifeq(member(X1,b),true,member(X1,c),true) = true,
inference(orient,[status(thm)],[t39216]) ).
cnf(f141,hypothesis,
subset(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_subset_b) ).
fof(f141_nnf,plain,
subset(a,b),
inference(nnf_transformation,[status(thm)],[f141]) ).
cnf(c141,plain,
subset(a,b),
inference(cnf_transformation,[status(esa)],[f141_nnf]) ).
cnf(t13,plain,
subset(a,b) = true,
inference(equality_encoding,[status(esa)],[c141]) ).
cnf(t1972,plain,
subset(a,b) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t1975,plain,
true = ifeq(true,true,ifeq(member(X1,a),true,member(X1,b),true),true),
inference(cp,[status(thm)],[t609,t1972]) ).
cnf(t39207,plain,
true = ifeq(member(X1,a),true,member(X1,b),true),
inference(step,[status(thm)],[t1975,t256]) ).
cnf(t37126,plain,
ifeq(member(X1,a),true,member(X1,b),true) = true,
inference(orient,[status(thm)],[t39207]) ).
cnf(f67,axiom,
( member(f17(X,Y),X)
| subset(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2) ).
fof(f67_nnf,plain,
! [X,Y] :
( member(f17(X,Y),X)
| subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [X,Y] :
( member(f17(X,Y),X)
| subset(X,Y) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( member(f17(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t58,plain,
or(subset(X1,X2),member(f17(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t1753,plain,
or(subset(X1,X2),member(f17(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t58]) ).
cnf(f143,negated_conjecture,
~ subset(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_subset_c) ).
fof(f143_nnf,plain,
~ subset(a,c),
inference(nnf_transformation,[status(thm)],[f143]) ).
fof(f143_sk,plain,
~ subset(a,c),
inference(skolemisation,[status(esa)],[f143_nnf]) ).
cnf(c143,plain,
~ subset(a,c),
inference(cnf_transformation,[status(esa)],[f143_sk]) ).
cnf(t14,plain,
subset(a,c) = false,
inference(equality_encoding,[status(esa)],[c143]) ).
cnf(t674,plain,
subset(a,c) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t1754,plain,
true = or(false,member(f17(a,c),a)),
inference(cp,[status(thm)],[t1753,t674]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t265,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t37758,plain,
true = member(f17(a,c),a),
inference(step,[status(thm)],[t1754,t265]) ).
cnf(t3009,plain,
member(f17(a,c),a) = true,
inference(orient,[status(thm)],[t37758]) ).
cnf(t37127,plain,
true = ifeq(true,true,member(f17(a,c),b),true),
inference(cp,[status(thm)],[t37126,t3009]) ).
cnf(t39208,plain,
true = member(f17(a,c),b),
inference(step,[status(thm)],[t37127,t256]) ).
cnf(t37129,plain,
member(f17(a,c),b) = true,
inference(orient,[status(thm)],[t39208]) ).
cnf(t37203,plain,
true = ifeq(true,true,member(f17(a,c),c),true),
inference(cp,[status(thm)],[t37202,t37129]) ).
cnf(t39217,plain,
true = member(f17(a,c),c),
inference(step,[status(thm)],[t37203,t256]) ).
cnf(t37205,plain,
member(f17(a,c),c) = true,
inference(orient,[status(thm)],[t39217]) ).
cnf(t37209,plain,
true = ifeq(true,true,subset(a,c),true),
inference(cp,[status(thm)],[t522,t37205]) ).
cnf(t39218,plain,
true = subset(a,c),
inference(step,[status(thm)],[t37209,t256]) ).
cnf(t39219,plain,
true = false,
inference(step,[status(thm)],[t39218,t674]) ).
cnf(t37230,plain,
false = true,
inference(orient,[status(thm)],[t39219]) ).
cnf(f30,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f30_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f57,axiom,
~ member(Z,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f57_nnf,plain,
! [Z] : ~ member(Z,empty_set),
inference(nnf_transformation,[status(thm)],[f57]) ).
fof(f57_sk,plain,
! [Z] : ~ member(Z,empty_set),
inference(skolemisation,[status(esa)],[f57_nnf]) ).
cnf(c57,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f57_sk]) ).
cnf(f70,axiom,
( X != Y
| ~ proper_subset(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proper_subset2) ).
fof(f70_nnf,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [X,Y] :
( X != Y
| ~ proper_subset(X,Y) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f94,axiom,
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint1) ).
fof(f94_nnf,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
! [X,Y,U] :
( ~ member(U,Y)
| ~ member(U,X)
| ~ disjoint(X,Y) ),
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c30,c57,c70,c94,c143]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37230]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:19:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 48.79/6.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.79/6.68 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------