%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Sun Sep 27 08:45:46 AM UTC 2026
% Result : Theorem 0.48s 0.53s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 29 unt; 0 def)
% Number of atoms : 89 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 26 ~; 19 |; 7 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 1 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('theBenchmark.p',redefinition_k5_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t15_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
file('theBenchmark.p',t15_pre_topc) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t22_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ),
file('theBenchmark.p',t22_pre_topc) ).
fof(t22_pre_topc_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ),
inference(assume_negation,[status(cth)],[t22_pre_topc]) ).
cnf(c_71,plain,
( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B
| ~ element(B,powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[t15_pre_topc]) ).
fof(nnf_70,plain,
? [A] :
( ? [B] :
( subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) != B
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t22_pre_topc_neg]) ).
fof(sk_t22_pre_topc_neg,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)) != sK1
& element(sK1,powerset(the_carrier(sK0)))
& one_sorted_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_70]) ).
cnf(c_72,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_pre_topc_neg]) ).
cnf(c_75,plain,
( the_carrier(A) = cast_as_carrier_subset(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
cnf(c_76,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_78,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_79,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_76,c_78]) ).
cnf(c_80,negated_conjecture,
subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)) != sK1,
inference(split_conjunct,[status(thm)],[sk_t22_pre_topc_neg]) ).
cnf(c_81,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t22_pre_topc_neg]) ).
cnf(c_88,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_89,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_95,plain,
( set_difference(A,C) = subset_difference(B,A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k6_subset_1]) ).
cnf(c_96,plain,
( subset_difference(B,A,C) = set_difference(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_97,plain,
( subset_intersection2(B,A,C) = set_intersection2(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k5_subset_1]) ).
cnf(c_98,plain,
( subset_intersection2(B,A,C) = set_difference(A,set_difference(A,C))
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(paramod,[status(thm)],[c_89,c_97]) ).
cnf(c_179,plain,
( element(subset_difference(B,A,C),powerset(B))
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[dt_k6_subset_1]) ).
cnf(c_182,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_993,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(B,A),
inference(paramod,[status(thm)],[c_89,c_182]) ).
cnf(c_183,plain,
set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)),
inference(paramod,[status(thm)],[c_89,c_993]) ).
cnf(c_209,negated_conjecture,
( subset_intersection2(the_carrier(sK0),A,cast_as_carrier_subset(sK0)) = A
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_71,c_72]) ).
cnf(c_215,negated_conjecture,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(resolve,[status(thm)],[c_75,c_72]) ).
cnf(c_216,negated_conjecture,
cast_as_carrier_subset(sK0) = the_carrier(sK0),
inference(copy,[status(thm)],[c_215]) ).
cnf(c_223,negated_conjecture,
( subset_intersection2(the_carrier(sK0),A,the_carrier(sK0)) = A
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(paramod,[status(thm)],[c_216,c_209]) ).
cnf(c_994,negated_conjecture,
subset_difference(the_carrier(sK0),the_carrier(sK0),subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)) != sK1,
inference(paramod,[status(thm)],[c_216,c_80]) ).
cnf(c_224,negated_conjecture,
subset_difference(the_carrier(sK0),the_carrier(sK0),subset_difference(the_carrier(sK0),the_carrier(sK0),sK1)) != sK1,
inference(paramod,[status(thm)],[c_216,c_994]) ).
cnf(c_230,plain,
( subset_difference(B,B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_96,c_79]) ).
cnf(c_233,plain,
( subset_intersection2(the_carrier(sK0),sK1,A) = set_difference(sK1,set_difference(sK1,A))
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_98,c_81]) ).
cnf(c_268,plain,
( element(subset_difference(B,B,A),powerset(B))
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_179,c_79]) ).
cnf(c_361,plain,
subset_intersection2(the_carrier(sK0),sK1,the_carrier(sK0)) = sK1,
inference(resolve,[status(thm)],[c_223,c_81]) ).
cnf(c_376,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) = set_difference(the_carrier(sK0),sK1),
inference(resolve,[status(thm)],[c_230,c_81]) ).
cnf(c_377,negated_conjecture,
subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK1)) != sK1,
inference(paramod,[status(thm)],[c_376,c_224]) ).
cnf(c_995,plain,
subset_intersection2(the_carrier(sK0),sK1,the_carrier(sK0)) = set_difference(sK1,set_difference(sK1,the_carrier(sK0))),
inference(resolve,[status(thm)],[c_233,c_79]) ).
cnf(c_996,plain,
sK1 = set_difference(sK1,set_difference(sK1,the_carrier(sK0))),
inference(paramod,[status(thm)],[c_361,c_995]) ).
cnf(c_420,plain,
set_difference(sK1,set_difference(sK1,the_carrier(sK0))) = sK1,
inference(copy,[status(thm)],[c_996]) ).
cnf(c_997,negated_conjecture,
element(subset_difference(the_carrier(sK0),the_carrier(sK0),sK1),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_268,c_81]) ).
cnf(c_527,negated_conjecture,
element(set_difference(the_carrier(sK0),sK1),powerset(the_carrier(sK0))),
inference(paramod,[status(thm)],[c_376,c_997]) ).
cnf(c_998,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK1)) = set_difference(the_carrier(sK0),set_difference(the_carrier(sK0),sK1)),
inference(resolve,[status(thm)],[c_527,c_230]) ).
cnf(c_999,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK1)) = set_difference(sK1,set_difference(sK1,the_carrier(sK0))),
inference(paramod,[status(thm)],[c_183,c_998]) ).
cnf(c_1000,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK1)) = sK1,
inference(paramod,[status(thm)],[c_420,c_999]) ).
cnf(c_992,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_377,c_1000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 09:10:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1179156 was started by sandbox2 on n020,
% 0.10/0.37 % Sat Sep 26 09:10:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.48/0.53
% 0.48/0.53 % SZS status Theorem for theBenchmark
% 0.48/0.53
% 0.48/0.53 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.48/0.53 % Length of proof is 41.
% 0.48/0.53 % Level of proof is 7.
% 0.48/0.53 % Maximum clause weight is 38.000.
% 0.48/0.53 % Given clauses 307.
% 0.48/0.53
% 0.48/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------