%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU089+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 19.98s 23.31s
% Output : Proof 19.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 38 unt; 0 def)
% Number of atoms : 148 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 68 ~; 18 |; 53 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 78 ( 3 sgn 45 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f50_nnf,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c133,plain,
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(hi120,axiom,
ifeq(finite(X0),true,ifeq(finite(X1),true,finite(cartesian_product2(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c133]) ).
fof(f52,conjecture,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
fof(f52_neg,negated_conjecture,
~ ! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
? [A,B,C] :
( ~ finite(cartesian_product3(A,B,C))
& finite(C)
& finite(B)
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
( ~ finite(cartesian_product3(sk26,sk27,sk28))
& finite(sk28)
& finite(sk27)
& finite(sk26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk26,sk27,sk28])],[f52_nnf]) ).
cnf(c135,plain,
finite(sk26),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi122,negated_conjecture,
finite(sk26) = true,
inference(equality_encoding,[status(esa)],[c135]) ).
cnf(c136,plain,
finite(sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi123,negated_conjecture,
finite(sk27) = true,
inference(equality_encoding,[status(esa)],[c136]) ).
cnf(h43,plain,
finite(cartesian_product2(sk26,sk27)) = true,
inference(hyper_resolution,[status(thm)],[hi120,hi122,hi123]) ).
cnf(c137,plain,
finite(sk28),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi124,negated_conjecture,
finite(sk28) = true,
inference(equality_encoding,[status(esa)],[c137]) ).
cnf(h482,plain,
finite(cartesian_product2(cartesian_product2(sk26,sk27),sk28)) = true,
inference(hyper_resolution,[status(thm)],[hi120,h43,hi124]) ).
cnf(c138,plain,
~ finite(cartesian_product3(sk26,sk27,sk28)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi140,negated_conjecture,
ifeq(finite(cartesian_product3(sk26,sk27,sk28)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c138]) ).
fof(f13,axiom,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(f13_nnf,plain,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c26,plain,
cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi39,axiom,
cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t15,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi140,h482,hi39]) ).
cnf(t678,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(f17,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f17_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c32,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f23,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f23_nnf,plain,
~ empty(positive_rationals),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ empty(positive_rationals),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c46,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f24,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(f24_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( natural(sk1)
& ordinal(sk1)
& epsilon_connected(sk1)
& epsilon_transitive(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f24_nnf]) ).
cnf(c47,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f25_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f25_nnf]) ).
cnf(c52,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f33,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(f33_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
( ordinal(sk10)
& epsilon_connected(sk10)
& epsilon_transitive(sk10)
& ~ empty(sk10)
& element(sk10,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f33_nnf]) ).
cnf(c72,plain,
~ empty(sk10),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f38,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f38_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( relation(sk15)
& ~ empty(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f38_nnf]) ).
cnf(c100,plain,
~ empty(sk15),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f40,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f40_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
~ empty(sk17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f40_nnf]) ).
cnf(c104,plain,
~ empty(sk17),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f44,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f44_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
( ordinal(sk21)
& epsilon_connected(sk21)
& epsilon_transitive(sk21)
& ~ empty(sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21])],[f44_nnf]) ).
cnf(c117,plain,
~ empty(sk21),
inference(cnf_transformation,[status(esa)],[f44_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(c143,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(c145,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,c32,c46,c47,c52,c72,c100,c104,c117,c138,c143,c145]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t678]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/20.38 % Computer : n016.cluster.edu
% 0.10/20.38 % Model : x86_64 x86_64
% 0.10/20.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.38 % Memory : 8046.5625MB
% 0.10/20.38 % OS : Linux 6.8.0-71-generic
% 0.10/20.38 % CPULimit : 300
% 0.10/20.38 % WCLimit : 300
% 0.10/20.38 % DateTime : Thu Sep 24 12:48:34 UTC 2026
% 0.10/20.38 % CPUTime :
% 0.10/20.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.98/23.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.98/23.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------