%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU140+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 : n002.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 02:51:03 PM UTC 2026
% Result : Theorem 0.15s 16.02s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 75 unt; 0 def)
% Number of atoms : 153 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 92 ( 47 ~; 27 |; 11 &)
% ( 1 <=>; 6 =>; 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; 8 con; 0-4 aty)
% Number of variables : 121 ( 3 sgn 54 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f14_neg,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ~ disjoint(sk2,sk4)
& disjoint(sk3,sk4)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f14_nnf]) ).
cnf(c17,plain,
~ disjoint(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t20,plain,
ifeq(disjoint(sk2,sk4),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t411,plain,
ifeq(disjoint(sk2,sk4),true,false,true) = true,
inference(orient,[status(thm)],[t20]) ).
fof(f10,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f10_nnf,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c11,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t24,plain,
ifeq(disjoint(X1,X2),true,disjoint(X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t410,plain,
ifeq(disjoint(X1,X2),true,disjoint(X2,X1),true) = true,
inference(orient,[status(thm)],[t24]) ).
fof(f2,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t26,plain,
ifeq(set_intersection2(X1,X2),empty_set,disjoint(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t389,plain,
ifeq(set_intersection2(X1,X2),empty_set,disjoint(X1,X2),true) = true,
inference(orient,[status(thm)],[t26]) ).
fof(f17,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f17_nnf,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c20,plain,
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi14,axiom,
ifeq(empty(X0),true,ifeq(empty(X1),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c20]) ).
fof(f5,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f5_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c6,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi3,axiom,
empty(empty_set) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f7,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f7_nnf,plain,
? [A] : empty(A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
empty(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f7_nnf]) ).
cnf(c8,plain,
empty(sk0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,axiom,
empty(sk0) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t0,plain,
sk0 = empty_set,
inference(hyper_resolution,[status(thm)],[hi14,hi3,hi5]) ).
cnf(t440,plain,
empty_set = sk0,
inference(orient,[status(thm)],[t0]) ).
cnf(t552,plain,
ifeq(set_intersection2(X1,X2),sk0,disjoint(X1,X2),true) = true,
inference(step,[status(thm)],[t389,t440]) ).
cnf(t450,plain,
ifeq(set_intersection2(X1,X2),sk0,disjoint(X1,X2),true) = true,
inference(rw,[status(thm)],[t552]) ).
cnf(t519,plain,
ifeq(set_intersection2(X1,X2),sk0,disjoint(X1,X2),true) = true,
inference(orient,[status(thm)],[t450]) ).
fof(f13,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f13_nnf,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t21,plain,
ifeq(subset(X1,empty_set),true,X1,empty_set) = empty_set,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t433,plain,
ifeq(subset(X1,empty_set),true,X1,empty_set) = empty_set,
inference(orient,[status(thm)],[t21]) ).
cnf(t549,plain,
ifeq(subset(X1,sk0),true,X1,empty_set) = empty_set,
inference(step,[status(thm)],[t433,t440]) ).
cnf(t550,plain,
ifeq(subset(X1,sk0),true,X1,sk0) = empty_set,
inference(step,[status(thm)],[t549,t440]) ).
cnf(t551,plain,
ifeq(subset(X1,sk0),true,X1,sk0) = sk0,
inference(step,[status(thm)],[t550,t440]) ).
cnf(t449,plain,
ifeq(subset(X1,sk0),true,X1,sk0) = sk0,
inference(rw,[status(thm)],[t551]) ).
cnf(t485,plain,
ifeq(subset(X1,sk0),true,X1,sk0) = sk0,
inference(orient,[status(thm)],[t449]) ).
fof(f11,axiom,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f11_nnf,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi8,axiom,
ifeq(subset(X0,X1),true,subset(set_intersection2(X0,X2),set_intersection2(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(c15,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi11,negated_conjecture,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t23,plain,
subset(set_intersection2(sk2,X1),set_intersection2(sk3,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi11]) ).
cnf(t383,plain,
subset(set_intersection2(sk2,X1),set_intersection2(sk3,X1)) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t17,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t56,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t17]) ).
cnf(t387,plain,
true = subset(set_intersection2(sk2,X1),set_intersection2(X1,sk3)),
inference(cp,[status(thm)],[t383,t56]) ).
cnf(t473,plain,
subset(set_intersection2(sk2,X1),set_intersection2(X1,sk3)) = true,
inference(orient,[status(thm)],[t387]) ).
cnf(c2,plain,
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(disjoint(X0,X1),true,set_intersection2(X0,X1),empty_set) = empty_set,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c16,plain,
disjoint(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi12,negated_conjecture,
disjoint(sk3,sk4) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t12,plain,
set_intersection2(sk3,sk4) = empty_set,
inference(hyper_resolution,[status(thm)],[hi1,hi12]) ).
cnf(t536,plain,
set_intersection2(sk4,sk3) = empty_set,
inference(step,[status(thm)],[t12,t56]) ).
cnf(t60,plain,
set_intersection2(sk4,sk3) = empty_set,
inference(orient,[status(thm)],[t536]) ).
cnf(t537,plain,
set_intersection2(sk4,sk3) = sk0,
inference(step,[status(thm)],[t60,t440]) ).
cnf(t441,plain,
set_intersection2(sk4,sk3) = sk0,
inference(orient,[status(thm)],[t537]) ).
cnf(t477,plain,
true = subset(set_intersection2(sk2,sk4),sk0),
inference(cp,[status(thm)],[t473,t441]) ).
cnf(t556,plain,
true = subset(set_intersection2(sk4,sk2),sk0),
inference(step,[status(thm)],[t477,t56]) ).
cnf(t479,plain,
subset(set_intersection2(sk4,sk2),sk0) = true,
inference(orient,[status(thm)],[t556]) ).
cnf(t486,plain,
sk0 = ifeq(true,true,set_intersection2(sk4,sk2),sk0),
inference(cp,[status(thm)],[t485,t479]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t53,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t558,plain,
sk0 = set_intersection2(sk4,sk2),
inference(step,[status(thm)],[t486,t53]) ).
cnf(t487,plain,
set_intersection2(sk4,sk2) = sk0,
inference(orient,[status(thm)],[t558]) ).
cnf(t521,plain,
true = ifeq(sk0,sk0,disjoint(sk4,sk2),true),
inference(cp,[status(thm)],[t519,t487]) ).
cnf(t564,plain,
true = disjoint(sk4,sk2),
inference(step,[status(thm)],[t521,t53]) ).
cnf(t524,plain,
disjoint(sk4,sk2) = true,
inference(orient,[status(thm)],[t564]) ).
cnf(t525,plain,
true = ifeq(true,true,disjoint(sk2,sk4),true),
inference(cp,[status(thm)],[t410,t524]) ).
cnf(t565,plain,
true = disjoint(sk2,sk4),
inference(step,[status(thm)],[t525,t53]) ).
cnf(t527,plain,
disjoint(sk2,sk4) = true,
inference(orient,[status(thm)],[t565]) ).
cnf(t566,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t411,t527]) ).
cnf(t567,plain,
false = true,
inference(step,[status(thm)],[t566,t53]) ).
cnf(t530,plain,
false = true,
inference(rw,[status(thm)],[t567]) ).
cnf(t531,plain,
false = true,
inference(orient,[status(thm)],[t530]) ).
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]) ).
fof(f8,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f8_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f8_nnf]) ).
cnf(c9,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f16,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f16_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c19,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c9,c17,c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t531]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/15.40 % Computer : n002.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.10/15.40 % CPULimit : 300
% 0.10/15.40 % WCLimit : 300
% 0.10/15.40 % DateTime : Thu Sep 24 12:57:35 UTC 2026
% 0.10/15.40 % CPUTime :
% 0.10/15.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/16.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/16.02 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------