%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:51:37 PM UTC 2026
% Result : Theorem 8.26s 6.63s
% Output : Proof 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 32 unt; 0 def)
% Number of atoms : 150 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 152 ( 73 ~; 23 |; 50 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 70 ( 3 sgn 40 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f48,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f48_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c134,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(hi120,axiom,
ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c134]) ).
fof(f45,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f45_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
( ~ finite(sk26)
& finite(sk27)
& subset(sk26,sk27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27])],[f45_nnf]) ).
cnf(c128,plain,
subset(sk26,sk27),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi115,negated_conjecture,
subset(sk26,sk27) = true,
inference(equality_encoding,[status(esa)],[c128]) ).
cnf(h69,plain,
element(sk26,powerset(sk27)) = true,
inference(hyper_resolution,[status(thm)],[hi120,hi115]) ).
fof(f7,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f7_nnf,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi11,axiom,
ifeq(finite(X0),true,ifeq(element(X1,powerset(X0)),true,finite(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c129,plain,
finite(sk27),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi116,negated_conjecture,
finite(sk27) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(h158,plain,
finite(sk26) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi116,h69]) ).
cnf(c130,plain,
~ finite(sk26),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi133,negated_conjecture,
ifeq(finite(sk26),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c130]) ).
cnf(t15,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi133,h158]) ).
cnf(t667,plain,
false = true,
inference(orient,[status(thm)],[t15]) ).
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(f14,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f14_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c29,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f18,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f18_nnf,plain,
~ empty(positive_rationals),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ empty(positive_rationals),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c41,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f19,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f19_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( natural(sk1)
& ordinal(sk1)
& epsilon_connected(sk1)
& epsilon_transitive(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f19_nnf]) ).
cnf(c42,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f20_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f20_nnf]) ).
cnf(c47,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f28,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f28_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
( ordinal(sk10)
& epsilon_connected(sk10)
& epsilon_transitive(sk10)
& ~ empty(sk10)
& element(sk10,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f28_nnf]) ).
cnf(c67,plain,
~ empty(sk10),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f33,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f33_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
( relation(sk15)
& ~ empty(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f33_nnf]) ).
cnf(c95,plain,
~ empty(sk15),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f35,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f35_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ empty(sk17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f35_nnf]) ).
cnf(c99,plain,
~ empty(sk17),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f39,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f39_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
( ordinal(sk21)
& epsilon_connected(sk21)
& epsilon_transitive(sk21)
& ~ empty(sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21])],[f39_nnf]) ).
cnf(c112,plain,
~ empty(sk21),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f50,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f50_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c136,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
fof(f52,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f52_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c138,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c29,c41,c42,c47,c67,c95,c99,c112,c130,c136,c138]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t667]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n014.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 13:34:39 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.26/6.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.26/6.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------