%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU085+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 : n016.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 9.35s 1.74s
% Output : Proof 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 28 unt; 0 def)
% Number of atoms : 126 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 65 ~; 15 |; 44 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 61 ( 6 sgn 34 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f13_nnf,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c26,plain,
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi21,axiom,
ifeq(finite(X0),true,finite(set_difference(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
fof(f48,conjecture,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
fof(f48_neg,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f48_nnf,plain,
? [A,B] :
( ~ finite(set_difference(A,B))
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f48_neg]) ).
fof(f48_sk,plain,
( ~ finite(set_difference(sk26,sk27))
& finite(sk26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f48_nnf]) ).
cnf(c131,plain,
finite(sk26),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(hi118,negated_conjecture,
finite(sk26) = true,
inference(equality_encoding,[status(esa)],[c131]) ).
cnf(h208,plain,
finite(set_difference(sk26,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi118]) ).
cnf(c132,plain,
~ finite(set_difference(sk26,sk27)),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(hi138,negated_conjecture,
ifeq(finite(set_difference(sk26,sk27)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c132]) ).
cnf(t15,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi138,h208]) ).
cnf(t760,plain,
false = true,
inference(orient,[status(thm)],[t15]) ).
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(f15,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c30,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f20,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f20_nnf,plain,
~ empty(positive_rationals),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ empty(positive_rationals),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c43,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,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(f21_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( natural(sk1)
& ordinal(sk1)
& epsilon_connected(sk1)
& epsilon_transitive(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f21_nnf]) ).
cnf(c44,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f22,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f22_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f22_nnf]) ).
cnf(c49,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f30,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(f30_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
( ordinal(sk10)
& epsilon_connected(sk10)
& epsilon_transitive(sk10)
& ~ empty(sk10)
& element(sk10,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f30_nnf]) ).
cnf(c69,plain,
~ empty(sk10),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f35,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f35_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
( relation(sk15)
& ~ empty(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f35_nnf]) ).
cnf(c97,plain,
~ empty(sk15),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f37,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f37_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
~ empty(sk17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f37_nnf]) ).
cnf(c101,plain,
~ empty(sk17),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f41,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f41_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
( ordinal(sk21)
& epsilon_connected(sk21)
& epsilon_transitive(sk21)
& ~ empty(sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21])],[f41_nnf]) ).
cnf(c114,plain,
~ empty(sk21),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f56,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f56_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c141,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
fof(f58,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f58_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c143,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c30,c43,c44,c49,c69,c97,c101,c114,c132,c141,c143]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t760]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU085+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n016.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 12:47:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.35/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.35/1.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------