%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU306+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 02:51:40 PM UTC 2026
% Result : Theorem 3.96s 0.94s
% Output : Proof 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 78 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 15 |; 20 &)
% ( 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 42 ( 3 sgn 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f38_nnf,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c75,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi65,axiom,
ifeq(one_sorted_str(X0),true,cast_as_carrier_subset(X0),the_carrier(X0)) = the_carrier(X0),
inference(equality_encoding,[status(esa)],[c75]) ).
fof(f39,conjecture,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f39_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f39_nnf,plain,
? [A] :
( cast_as_carrier_subset(A) != the_carrier(A)
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f39_neg]) ).
fof(f39_sk,plain,
( cast_as_carrier_subset(sk5) != the_carrier(sk5)
& one_sorted_str(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f39_nnf]) ).
cnf(c76,plain,
one_sorted_str(sk5),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi66,negated_conjecture,
one_sorted_str(sk5) = true,
inference(equality_encoding,[status(esa)],[c76]) ).
cnf(h2,plain,
cast_as_carrier_subset(sk5) = the_carrier(sk5),
inference(hyper_resolution,[status(thm)],[hi65,hi66]) ).
cnf(c77,plain,
cast_as_carrier_subset(sk5) != the_carrier(sk5),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi72,negated_conjecture,
ifeq(cast_as_carrier_subset(sk5),the_carrier(sk5),false,true) = true,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi72,h2]) ).
cnf(t379,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f6,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(f6_nnf,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
( v5_membered(sk0)
& v4_membered(sk0)
& v3_membered(sk0)
& v2_membered(sk0)
& v1_membered(sk0)
& ~ empty(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c6,plain,
~ empty(sk0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f20,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f20_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c50,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f27,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f27_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c63,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f32,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f32_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c68,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c50,c63,c68,c77]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t379]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU306+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 13:37:28 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.96/0.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.96/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------