%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL064-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 06:57:35 AM UTC 2026
% Result : Unsatisfiable 66.17s 10.04s
% Output : CNFRefutation 66.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(t_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(t,VAR_0),VAR_1) = apply(VAR_1,VAR_0),
file('theBenchmark.p',t_definition) ).
cnf(c_2,plain,
apply(apply(t,A),B) = apply(B,A),
inference(clausify,[status(thm)],[t_definition]) ).
fof(prove_v_combinator,axiom,
! [VAR_0] : apply(apply(apply(VAR_0,f(VAR_0)),g(VAR_0)),h(VAR_0)) != apply(apply(h(VAR_0),f(VAR_0)),g(VAR_0)),
file('theBenchmark.p',prove_v_combinator) ).
cnf(c_3,plain,
apply(apply(apply(A,f(A)),g(A)),h(A)) != apply(apply(h(A),f(A)),g(A)),
inference(clausify,[status(thm)],[prove_v_combinator]) ).
cnf(c_4,plain,
apply(apply(h(A),f(A)),g(A)) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_5,plain,
apply(apply(apply(b,A),apply(apply(b,B),C)),D) = apply(A,apply(B,apply(C,D))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
apply(apply(apply(apply(apply(b,b),A),B),C),D) = apply(apply(A,B),apply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
apply(apply(apply(b,apply(t,A)),B),C) = apply(apply(B,C),A),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_31,plain,
apply(apply(apply(b,apply(t,A)),apply(apply(b,B),C)),D) = apply(apply(B,apply(C,D)),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_88,plain,
apply(apply(apply(apply(apply(b,b),t),A),B),C) = apply(apply(B,C),A),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_250,plain,
apply(apply(apply(b,apply(t,g(A))),h(A)),f(A)) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(paramod,[status(thm)],[c_11,c_4]) ).
cnf(c_6221,plain,
apply(apply(apply(apply(b,A),B),C),D) = apply(apply(t,D),apply(A,apply(B,C))),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_254,plain,
apply(apply(apply(apply(b,A),B),C),D) = apply(apply(A,apply(B,C)),D),
inference(paramod,[status(thm)],[c_2,c_6221]) ).
cnf(c_1497,plain,
apply(apply(apply(apply(apply(b,b),t),g(A)),h(A)),f(A)) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(paramod,[status(thm)],[c_1,c_250]) ).
cnf(c_4239,plain,
apply(apply(apply(apply(apply(b,apply(t,A)),apply(apply(b,b),B)),C),D),E) = apply(apply(apply(B,C),apply(A,D)),E),
inference(paramod,[status(thm)],[c_31,c_254]) ).
cnf(c_6219,plain,
apply(apply(apply(apply(apply(b,b),t),f(A)),apply(apply(apply(b,b),t),g(A))),h(A)) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(paramod,[status(thm)],[c_88,c_1497]) ).
cnf(c_6222,plain,
apply(apply(apply(B,C),apply(A,D)),E) = apply(apply(apply(apply(apply(b,apply(t,A)),apply(apply(b,b),B)),C),D),E),
inference(copy,[status(thm)],[c_4239]) ).
cnf(c_6220,plain,
$false,
inference(resolve,[status(thm)],[c_6219,c_6222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL064-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n009.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 23:10:30 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 1380153 was started by sandbox on n009,
% 0.18/0.43 % Sat Sep 26 23:10:30 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 66.17/10.04
% 66.17/10.04 % SZS status Unsatisfiable for theBenchmark
% 66.17/10.04
% 66.17/10.04 % Proof 1 at 1.27 (+ 0.26) seconds.
% 66.17/10.04 % Length of proof is 15.
% 66.17/10.04 % Level of proof is 5.
% 66.17/10.04 % Maximum clause weight is 82.000.
% 66.17/10.04 % Given clauses 72.
% 66.17/10.04
% 66.17/10.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------