%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL060-1 : 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 06:57:33 AM UTC 2026
% Result : Unsatisfiable 12.02s 2.08s
% Output : CNFRefutation 12.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 23 ( 3 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 : 111 ( 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_q_combinator,axiom,
! [VAR_0] : apply(apply(apply(VAR_0,f(VAR_0)),g(VAR_0)),h(VAR_0)) != apply(g(VAR_0),apply(f(VAR_0),h(VAR_0))),
file('theBenchmark.p',prove_q_combinator) ).
cnf(c_3,plain,
apply(apply(apply(A,f(A)),g(A)),h(A)) != apply(g(A),apply(f(A),h(A))),
inference(clausify,[status(thm)],[prove_q_combinator]) ).
cnf(c_3629,plain,
apply(apply(apply(b,A),apply(t,B)),C) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_4,plain,
apply(A,apply(apply(t,B),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_1,c_3629]) ).
cnf(c_5,plain,
apply(apply(apply(apply(t,A),b),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_6,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_8,plain,
apply(apply(t,A),apply(t,B)) = apply(A,B),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_15,plain,
apply(apply(apply(apply(t,f(A)),A),g(A)),h(A)) != apply(g(A),apply(f(A),h(A))),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3630,plain,
apply(apply(t,A),apply(B,C)) = apply(apply(apply(t,C),B),A),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_25,plain,
apply(apply(apply(t,A),B),C) = apply(apply(t,C),apply(B,A)),
inference(copy,[status(thm)],[c_3630]) ).
cnf(c_27,plain,
apply(apply(t,A),apply(apply(t,B),C)) = apply(apply(C,B),A),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_28,plain,
apply(A,apply(apply(apply(t,B),t),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_86,plain,
apply(apply(t,A),apply(apply(apply(t,B),b),C)) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_127,plain,
apply(apply(t,A),apply(apply(t,B),apply(b,C))) = apply(C,apply(B,A)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_540,plain,
apply(apply(t,h(A)),apply(apply(t,g(A)),apply(apply(t,f(A)),A))) != apply(g(A),apply(f(A),h(A))),
inference(paramod,[status(thm)],[c_27,c_15]) ).
cnf(c_3631,plain,
apply(apply(t,apply(A,B)),apply(t,C)) = apply(apply(apply(apply(t,B),t),A),C),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_3632,plain,
apply(apply(A,B),C) = apply(apply(apply(apply(t,B),t),A),C),
inference(paramod,[status(thm)],[c_8,c_3631]) ).
cnf(c_557,plain,
apply(apply(apply(apply(t,A),t),B),C) = apply(apply(B,A),C),
inference(copy,[status(thm)],[c_3632]) ).
cnf(c_3349,plain,
apply(apply(t,apply(A,B)),C) = apply(apply(t,B),apply(apply(t,A),apply(b,C))),
inference(paramod,[status(thm)],[c_127,c_2]) ).
cnf(c_3439,plain,
apply(apply(apply(t,A),B),C) = apply(apply(t,A),apply(apply(t,B),apply(b,apply(t,C)))),
inference(paramod,[status(thm)],[c_127,c_25]) ).
cnf(c_3633,plain,
apply(apply(apply(t,A),apply(apply(t,B),apply(b,apply(apply(t,C),t)))),D) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_127,c_557]) ).
cnf(c_3634,plain,
apply(apply(t,A),apply(apply(t,apply(apply(t,B),apply(b,apply(apply(t,C),t)))),apply(b,apply(t,D)))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3439,c_3633]) ).
cnf(c_3635,plain,
apply(apply(t,A),apply(apply(t,apply(b,apply(apply(t,C),t))),apply(apply(t,apply(t,B)),apply(b,apply(b,apply(t,D)))))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3349,c_3634]) ).
cnf(c_3636,plain,
apply(apply(t,A),apply(apply(t,apply(b,apply(apply(t,C),t))),apply(apply(t,B),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,D)))))))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3349,c_3635]) ).
cnf(c_3637,plain,
apply(apply(t,A),apply(apply(t,apply(apply(t,C),t)),apply(apply(t,b),apply(b,apply(apply(t,B),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,D)))))))))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3349,c_3636]) ).
cnf(c_3638,plain,
apply(apply(t,A),apply(apply(t,t),apply(apply(t,apply(t,C)),apply(b,apply(apply(t,b),apply(b,apply(apply(t,B),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,D)))))))))))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3349,c_3637]) ).
cnf(c_3639,plain,
apply(apply(t,A),apply(apply(t,t),apply(apply(t,C),apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,B),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,D)))))))))))))) = apply(apply(apply(B,A),C),D),
inference(paramod,[status(thm)],[c_3349,c_3638]) ).
cnf(c_3526,plain,
apply(apply(apply(A,B),C),D) = apply(apply(t,B),apply(apply(t,t),apply(apply(t,C),apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,A),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,D)))))))))))))),
inference(copy,[status(thm)],[c_3639]) ).
cnf(c_3640,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(apply(t,apply(t,C)),b),b))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_86,c_127]) ).
cnf(c_3641,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(apply(t,C),apply(apply(t,t),apply(b,b))),b))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_3349,c_3640]) ).
cnf(c_3642,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),apply(apply(t,t),apply(apply(t,apply(apply(t,t),apply(b,b))),apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,b)))))))))))))))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_3526,c_3641]) ).
cnf(c_3643,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),apply(apply(t,t),apply(apply(t,apply(b,b)),apply(apply(t,apply(t,t)),apply(b,apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,b)))))))))))))))))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_3349,c_3642]) ).
cnf(c_3644,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),apply(apply(t,t),apply(apply(t,apply(b,b)),apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,b)))))))))))))))))))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_3349,c_3643]) ).
cnf(c_3627,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),apply(apply(t,t),apply(apply(t,b),apply(apply(t,b),apply(b,apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(apply(t,t),apply(b,apply(b,apply(apply(t,b),apply(b,apply(apply(t,t),apply(apply(t,t),apply(b,apply(b,apply(b,apply(t,b)))))))))))))))))))))) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_3349,c_3644]) ).
cnf(c_3628,plain,
$false,
inference(resolve,[status(thm)],[c_3627,c_540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL060-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n009.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 23:09:44 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 1378138 was started by sandbox on n009,
% 0.18/0.46 % Sat Sep 26 23:09:44 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 12.02/2.08
% 12.02/2.08 % SZS status Unsatisfiable for theBenchmark
% 12.02/2.08
% 12.02/2.08 % Proof 1 at 1.33 (+ 0.24) seconds.
% 12.02/2.08 % Length of proof is 20.
% 12.02/2.08 % Level of proof is 6.
% 12.02/2.08 % Maximum clause weight is 75.000.
% 12.02/2.08 % Given clauses 72.
% 12.02/2.08
% 12.02/2.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------