%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET907+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 : n005.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 02:44:15 PM UTC 2026
% Result : Theorem 4.16s 1.08s
% Output : Proof 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 65 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 14 |; 11 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f10_nnf,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(in(X0,X1),true,ifeq(in(X2,X1),true,subset(unordered_pair(X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f11,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B,C] :
( set_union2(unordered_pair(A,C),B) != B
& in(C,B)
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( set_union2(unordered_pair(sk2,sk4),sk3) != sk3
& in(sk4,sk3)
& in(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f11_nnf]) ).
cnf(c13,plain,
in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
in(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c14,plain,
in(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,negated_conjecture,
in(sk4,sk3) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h4,plain,
subset(unordered_pair(sk2,sk4),sk3) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi11,hi12]) ).
fof(f9,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f9_nnf,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi7,axiom,
ifeq(subset(X0,X1),true,set_union2(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h11,plain,
set_union2(unordered_pair(sk2,sk4),sk3) = sk3,
inference(hyper_resolution,[status(thm)],[hi7,h4]) ).
cnf(c15,plain,
set_union2(unordered_pair(sk2,sk4),sk3) != sk3,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(set_union2(unordered_pair(sk2,sk4),sk3),sk3,false,true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi15,h11]) ).
cnf(t115,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f7,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f7_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c7,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c7,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t115]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.52 % Computer : n005.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Thu Sep 24 12:21:18 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.16/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.16/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------