%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET027-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 155.18s 20.65s
% Output : Proof 155.18s
% 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(t146,plain,
ifeq(member(f17(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t385,plain,
ifeq(member(f17(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t146]) ).
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(t217,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t472,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t217]) ).
cnf(f153,hypothesis,
subset(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_subset_c) ).
fof(f153_nnf,plain,
subset(b,c),
inference(nnf_transformation,[status(thm)],[f153]) ).
cnf(c153,plain,
subset(b,c),
inference(cnf_transformation,[status(esa)],[f153_nnf]) ).
cnf(t20,plain,
subset(b,c) = true,
inference(equality_encoding,[status(esa)],[c153]) ).
cnf(t2337,plain,
subset(b,c) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t2339,plain,
true = ifeq(true,true,ifeq(member(X1,b),true,member(X1,c),true),true),
inference(cp,[status(thm)],[t472,t2337]) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t32]) ).
cnf(t111013,plain,
true = ifeq(member(X1,b),true,member(X1,c),true),
inference(step,[status(thm)],[t2339,t256]) ).
cnf(t108096,plain,
ifeq(member(X1,b),true,member(X1,c),true) = true,
inference(orient,[status(thm)],[t111013]) ).
cnf(f152,hypothesis,
subset(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_subset_b) ).
fof(f152_nnf,plain,
subset(a,b),
inference(nnf_transformation,[status(thm)],[f152]) ).
cnf(c152,plain,
subset(a,b),
inference(cnf_transformation,[status(esa)],[f152_nnf]) ).
cnf(t18,plain,
subset(a,b) = true,
inference(equality_encoding,[status(esa)],[c152]) ).
cnf(t2345,plain,
subset(a,b) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t2347,plain,
true = ifeq(true,true,ifeq(member(X1,a),true,member(X1,b),true),true),
inference(cp,[status(thm)],[t472,t2345]) ).
cnf(t111014,plain,
true = ifeq(member(X1,a),true,member(X1,b),true),
inference(step,[status(thm)],[t2347,t256]) ).
cnf(t108097,plain,
ifeq(member(X1,a),true,member(X1,b),true) = true,
inference(orient,[status(thm)],[t111014]) ).
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(t100,plain,
or(subset(X1,X2),member(f17(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t2065,plain,
or(subset(X1,X2),member(f17(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(f154,negated_conjecture,
~ subset(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_subset_c) ).
fof(f154_nnf,plain,
~ subset(a,c),
inference(nnf_transformation,[status(thm)],[f154]) ).
fof(f154_sk,plain,
~ subset(a,c),
inference(skolemisation,[status(esa)],[f154_nnf]) ).
cnf(c154,plain,
~ subset(a,c),
inference(cnf_transformation,[status(esa)],[f154_sk]) ).
cnf(t19,plain,
subset(a,c) = false,
inference(equality_encoding,[status(esa)],[c154]) ).
cnf(t1944,plain,
subset(a,c) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t2066,plain,
true = or(false,member(f17(a,c),a)),
inference(cp,[status(thm)],[t2065,t1944]) ).
cnf(t16,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t275,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(t108542,plain,
true = member(f17(a,c),a),
inference(step,[status(thm)],[t2066,t275]) ).
cnf(t4890,plain,
member(f17(a,c),a) = true,
inference(orient,[status(thm)],[t108542]) ).
cnf(t108098,plain,
true = ifeq(true,true,member(f17(a,c),b),true),
inference(cp,[status(thm)],[t108097,t4890]) ).
cnf(t111015,plain,
true = member(f17(a,c),b),
inference(step,[status(thm)],[t108098,t256]) ).
cnf(t108099,plain,
member(f17(a,c),b) = true,
inference(orient,[status(thm)],[t111015]) ).
cnf(t108100,plain,
true = ifeq(true,true,member(f17(a,c),c),true),
inference(cp,[status(thm)],[t108096,t108099]) ).
cnf(t111016,plain,
true = member(f17(a,c),c),
inference(step,[status(thm)],[t108100,t256]) ).
cnf(t108128,plain,
member(f17(a,c),c) = true,
inference(orient,[status(thm)],[t111016]) ).
cnf(t108132,plain,
true = ifeq(true,true,subset(a,c),true),
inference(cp,[status(thm)],[t385,t108128]) ).
cnf(t111017,plain,
true = subset(a,c),
inference(step,[status(thm)],[t108132,t256]) ).
cnf(t111018,plain,
true = false,
inference(step,[status(thm)],[t111017,t1944]) ).
cnf(t108157,plain,
false = true,
inference(orient,[status(thm)],[t111018]) ).
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,c154]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t108157]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 09:18:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 155.18/20.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 155.18/20.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------