%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU204+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 : 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 : Sun Sep 27 08:45:24 AM UTC 2026
% Result : Theorem 8.00s 11.47s
% Output : CNFRefutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 142 ( 27 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 175 ( 70 ~; 71 |; 24 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 114 ( 3 sgn 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(t144_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t144_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
inference(assume_negation,[status(cth)],[t144_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(X3,D),A) )
| in(D,C) ) )
| relation_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X2,X0),A) )
| in(X0,C) )
& ( ? [X1] :
( in(X1,B)
& in(ordered_pair(X1,X0),A) )
| ~ in(X0,C) ) )
| relation_image(A,B) != C ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(sk_d13_relat_1_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK4(A,B,C)),A) )
| ~ in(sK4(A,B,C),C) )
& ( ( in(sK5(A,B,C),B)
& in(ordered_pair(sK5(A,B,C),sK4(A,B,C)),A) )
| in(sK4(A,B,C),C) ) )
| relation_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X2,X0),A) )
| in(X0,C) )
& ( ( in(sK0(A,B,C,X0),B)
& in(ordered_pair(sK0(A,B,C,X0),X0),A) )
| ~ in(X0,C) ) )
| relation_image(A,B) != C ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK5]),skolemize(X1,sK0(A,B,C,X0)),skolemize(D,sK4(A,B,C)),skolemize(X3,sK5(A,B,C))],[nnf_4]) ).
fof(sk_d13_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(ordered_pair(VAR_3,sK4(VAR_0,VAR_1,VAR_2)),VAR_0)
| ~ in(sK4(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK5(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK4(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK5(VAR_0,VAR_1,VAR_2),sK4(VAR_0,VAR_1,VAR_2)),VAR_0)
| in(sK4(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ in(VAR_4,VAR_1)
| ~ in(ordered_pair(VAR_4,VAR_3),VAR_0)
| in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(ordered_pair(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3),VAR_0)
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d13_relat_1_sk]) ).
cnf(c_40,plain,
( in(ordered_pair(sK0(A,B,C,D),D),A)
| ~ in(D,C)
| relation_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d13_relat_1]) ).
cnf(c_48,plain,
( ~ in(ordered_pair(D,C),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_relat_1]) ).
fof(nnf_39,plain,
? [A,B] :
( ~ subset(relation_image(B,A),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1_neg]) ).
fof(sk_t144_relat_1_neg,plain,
( ~ subset(relation_image(sK1,sK2),relation_rng(sK1))
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1)],[nnf_39]) ).
cnf(c_56,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t144_relat_1_neg]) ).
cnf(c_57,negated_conjecture,
( in(ordered_pair(sK0(sK1,A,B,C),C),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_56,c_40]) ).
cnf(c_64,negated_conjecture,
( ~ in(ordered_pair(C,B),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_56,c_48]) ).
cnf(c_118,negated_conjecture,
~ subset(relation_image(sK1,sK2),relation_rng(sK1)),
inference(split_conjunct,[status(thm)],[sk_t144_relat_1_neg]) ).
cnf(c_144,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
fof(nnf_5,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X3] :
( in(X3,B)
| ~ in(X3,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK3(A,B),B)
& in(sK3(A,B),A) )
| subset(A,B) )
& ( ! [X3] :
( in(X3,B)
| ~ in(X3,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(C,sK3(A,B))],[nnf_5]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_145,plain,
( ~ in(sK3(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_146,plain,
( in(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_148,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_194,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(C,B),singleton(C)),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(paramod,[status(thm)],[c_144,c_64]) ).
cnf(c_4669,negated_conjecture,
( in(unordered_pair(unordered_pair(sK0(sK1,A,B,C),C),singleton(sK0(sK1,A,B,C))),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_144,c_57]) ).
cnf(c_199,negated_conjecture,
( in(unordered_pair(unordered_pair(C,sK0(sK1,A,B,C)),singleton(sK0(sK1,A,B,C))),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_148,c_4669]) ).
cnf(c_278,negated_conjecture,
~ in(sK3(relation_image(sK1,sK2),relation_rng(sK1)),relation_rng(sK1)),
inference(resolve,[status(thm)],[c_145,c_118]) ).
cnf(c_280,plain,
in(sK3(relation_image(sK1,sK2),relation_rng(sK1)),relation_image(sK1,sK2)),
inference(resolve,[status(thm)],[c_146,c_118]) ).
cnf(c_380,plain,
( ~ in(unordered_pair(unordered_pair(B,C),singleton(C)),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(paramod,[status(thm)],[c_148,c_194]) ).
cnf(c_4670,negated_conjecture,
( in(unordered_pair(unordered_pair(sK3(relation_image(sK1,sK2),relation_rng(sK1)),sK0(sK1,A,relation_image(sK1,sK2),sK3(relation_image(sK1,sK2),relation_rng(sK1)))),singleton(sK0(sK1,A,relation_image(sK1,sK2),sK3(relation_image(sK1,sK2),relation_rng(sK1))))),sK1)
| relation_image(sK1,A) != relation_image(sK1,sK2) ),
inference(resolve,[status(thm)],[c_280,c_199]) ).
cnf(c_1045,negated_conjecture,
( in(unordered_pair(unordered_pair(sK3(relation_image(sK1,sK2),relation_rng(sK1)),sK0(sK1,A,relation_image(sK1,sK2),sK3(relation_image(sK1,sK2),relation_rng(sK1)))),singleton(sK0(sK1,A,relation_image(sK1,sK2),sK3(relation_image(sK1,sK2),relation_rng(sK1))))),sK1)
| relation_image(sK1,sK2) != relation_image(sK1,A) ),
inference(copy,[status(thm)],[c_4670]) ).
cnf(c_4671,plain,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(B)),sK1)
| in(A,relation_rng(sK1)) ),
inference(xxres,[status(thm)],[c_380]) ).
cnf(c_3841,plain,
~ in(unordered_pair(unordered_pair(sK3(relation_image(sK1,sK2),relation_rng(sK1)),A),singleton(A)),sK1),
inference(resolve,[status(thm)],[c_4671,c_278]) ).
cnf(c_3847,negated_conjecture,
relation_image(sK1,sK2) != relation_image(sK1,A),
inference(resolve,[status(thm)],[c_3841,c_1045]) ).
cnf(c_4668,plain,
$false,
inference(xxres,[status(thm)],[c_3847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n014.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 08:48:56 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 2686599 was started by sandbox2 on n014,
% 0.11/10.39 % Sat Sep 26 08:48:56 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.40
% 0.15/10.40 % From the command line: assign(max_seconds, 300).
% 8.00/11.47
% 8.00/11.47 % given #500 (T,wt=21): 1235 in(f4(c3,f8(c3)),c3). [resolve(1173,a,146,a)].
% 8.00/11.47
% 8.00/11.47 % SZS status Theorem for theBenchmark
% 8.00/11.47
% 8.00/11.47 % Proof 1 at 0.87 (+ 0.18) seconds.
% 8.00/11.47 % Length of proof is 25.
% 8.00/11.47 % Level of proof is 7.
% 8.00/11.47 % Maximum clause weight is 77.000.
% 8.00/11.47 % Given clauses 673.
% 8.00/11.47
% 8.00/11.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------