%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:51:02 PM UTC 2026
% Result : Theorem 97.21s 12.85s
% Output : Proof 97.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 36 unt; 0 def)
% Number of atoms : 156 ( 39 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 171 ( 81 ~; 50 |; 34 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 126 ( 11 sgn 61 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6_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)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk2(A,B),B)
& in(sk2(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f6_nnf]) ).
cnf(c19,plain,
( ~ in(sk2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t198,plain,
ifeq(in(sk2(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t373,plain,
ifeq(in(sk2(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t198]) ).
fof(f8,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f8_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk4(A,B,C),B)
& in(sk4(A,B,C),A)
& ~ in(sk4(A,B,C),C) )
| ( ( in(sk4(A,B,C),B)
| ~ in(sk4(A,B,C),A) )
& in(sk4(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f8_nnf]) ).
cnf(c29,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t216,plain,
ifeq(X1,set_difference(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t358,plain,
ifeq(X1,set_difference(X2,X3),ifeq(in(X4,X1),true,in(X4,X2),true),true) = true,
inference(orient,[status(thm)],[t216]) ).
cnf(t103,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t103]) ).
cnf(t359,plain,
true = ifeq(in(X1,set_difference(X2,X3)),true,in(X1,X2),true),
inference(cp,[status(thm)],[t358,t262]) ).
cnf(t38255,plain,
ifeq(in(X1,set_difference(X2,X3)),true,in(X1,X2),true) = true,
inference(orient,[status(thm)],[t359]) ).
cnf(c18,plain,
( in(sk2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t191,plain,
or(subset(X1,X2),in(sk2(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t279,plain,
or(subset(X1,X2),in(sk2(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t191]) ).
fof(f35,conjecture,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f35_neg,negated_conjecture,
~ ! [A,B] : subset(set_difference(A,B),A),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A,B] : ~ subset(set_difference(A,B),A),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
~ subset(set_difference(sk8,sk9),sk8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f35_nnf]) ).
cnf(c69,plain,
~ subset(set_difference(sk8,sk9),sk8),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t146,plain,
subset(set_difference(sk8,sk9),sk8) = false,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(t932,plain,
subset(set_difference(sk8,sk9),sk8) = false,
inference(orient,[status(thm)],[t146]) ).
cnf(t947,plain,
true = or(false,in(sk2(set_difference(sk8,sk9),sk8),set_difference(sk8,sk9))),
inference(cp,[status(thm)],[t279,t932]) ).
cnf(t21,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(t39292,plain,
true = in(sk2(set_difference(sk8,sk9),sk8),set_difference(sk8,sk9)),
inference(step,[status(thm)],[t947,t257]) ).
cnf(t1485,plain,
in(sk2(set_difference(sk8,sk9),sk8),set_difference(sk8,sk9)) = true,
inference(orient,[status(thm)],[t39292]) ).
cnf(t38264,plain,
true = ifeq(true,true,in(sk2(set_difference(sk8,sk9),sk8),sk8),true),
inference(cp,[status(thm)],[t38255,t1485]) ).
cnf(t39620,plain,
true = in(sk2(set_difference(sk8,sk9),sk8),sk8),
inference(step,[status(thm)],[t38264,t262]) ).
cnf(t38984,plain,
in(sk2(set_difference(sk8,sk9),sk8),sk8) = true,
inference(orient,[status(thm)],[t39620]) ).
cnf(t38990,plain,
true = ifeq(true,true,subset(set_difference(sk8,sk9),sk8),true),
inference(cp,[status(thm)],[t373,t38984]) ).
cnf(t39621,plain,
true = subset(set_difference(sk8,sk9),sk8),
inference(step,[status(thm)],[t38990,t262]) ).
cnf(t39622,plain,
true = false,
inference(step,[status(thm)],[t39621,t932]) ).
cnf(t39016,plain,
false = true,
inference(orient,[status(thm)],[t39622]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/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(f4,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c6,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c30,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f21,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f21_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ empty(sk6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f21_nnf]) ).
cnf(c52,plain,
~ empty(sk6),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f37,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f37_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk10(A,B),B)
& in(sk10(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f37_nnf]) ).
cnf(c73,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f40,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f40_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk11(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f40_nnf]) ).
cnf(c77,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f42,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f42_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c79,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c30,c52,c69,c73,c77,c79]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t39016]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:54:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 97.21/12.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.21/12.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------