%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU083+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:50:55 PM UTC 2026
% Result : Theorem 14.86s 2.34s
% Output : Proof 14.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 30 unt; 0 def)
% Number of atoms : 136 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 139 ( 68 ~; 18 |; 49 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-4 aty)
% Number of variables : 60 ( 3 sgn 34 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f61,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_finset_1) ).
fof(f61_nnf,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c147,plain,
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(hi131,axiom,
ifeq(finite(X0),true,ifeq(finite(X1),true,finite(set_union2(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c147]) ).
fof(f60,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).
fof(f60_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
inference(negated_conjecture,[status(cth)],[f60]) ).
fof(f60_nnf,plain,
? [A,B] :
( ~ finite(set_union2(A,B))
& finite(B)
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f60_neg]) ).
fof(f60_sk,plain,
( ~ finite(set_union2(sk26,sk27))
& finite(sk27)
& finite(sk26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f60_nnf]) ).
cnf(c144,plain,
finite(sk26),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(hi129,negated_conjecture,
finite(sk26) = true,
inference(equality_encoding,[status(esa)],[c144]) ).
cnf(c145,plain,
finite(sk27),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(hi130,negated_conjecture,
finite(sk27) = true,
inference(equality_encoding,[status(esa)],[c145]) ).
cnf(h311,plain,
finite(set_union2(sk26,sk27)) = true,
inference(hyper_resolution,[status(thm)],[hi131,hi129,hi130]) ).
cnf(c146,plain,
~ finite(set_union2(sk26,sk27)),
inference(cnf_transformation,[status(esa)],[f60_sk]) ).
cnf(hi143,negated_conjecture,
ifeq(finite(set_union2(sk26,sk27)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c146]) ).
cnf(t15,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi143,h311]) ).
cnf(t653,plain,
false = true,
inference(orient,[status(thm)],[t15]) ).
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f9,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f9_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c19,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f17,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f17_nnf,plain,
~ empty(positive_rationals),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ empty(positive_rationals),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c29,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f24,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f24_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c47,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f30,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c54,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f35,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f35_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
( finite(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f35_nnf]) ).
cnf(c59,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f46,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f46_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
( relation(sk12)
& ~ empty(sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f46_nnf]) ).
cnf(c98,plain,
~ empty(sk12),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f48,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f48_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
( natural(sk14)
& ordinal(sk14)
& epsilon_connected(sk14)
& epsilon_transitive(sk14)
& ~ empty(sk14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14])],[f48_nnf]) ).
cnf(c102,plain,
~ empty(sk14),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
fof(f49,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f49_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
( ordinal(sk15)
& epsilon_connected(sk15)
& epsilon_transitive(sk15)
& ~ empty(sk15)
& element(sk15,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f49_nnf]) ).
cnf(c108,plain,
~ empty(sk15),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
fof(f53,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f53_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
( ordinal(sk19)
& epsilon_connected(sk19)
& epsilon_transitive(sk19)
& ~ empty(sk19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19])],[f53_nnf]) ).
cnf(c128,plain,
~ empty(sk19),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
fof(f58,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f58_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
~ empty(sk24),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk24])],[f58_nnf]) ).
cnf(c140,plain,
~ empty(sk24),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c19,c29,c47,c54,c59,c98,c102,c108,c128,c140,c146]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t653]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU083+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:38:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.86/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.86/2.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------