%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL061-1 : 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 : n007.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 19.22s 2.86s
% Output : CNFRefutation 19.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 123 ( 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_q1_combinator,axiom,
! [VAR_0] : apply(apply(apply(VAR_0,f(VAR_0)),g(VAR_0)),h(VAR_0)) != apply(f(VAR_0),apply(h(VAR_0),g(VAR_0))),
file('theBenchmark.p',prove_q1_combinator) ).
cnf(c_3,plain,
apply(apply(apply(A,f(A)),g(A)),h(A)) != apply(f(A),apply(h(A),g(A))),
inference(clausify,[status(thm)],[prove_q1_combinator]) ).
cnf(c_4,plain,
apply(f(A),apply(h(A),g(A))) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_6072,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_5,plain,
apply(A,apply(apply(t,B),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_1,c_6072]) ).
cnf(c_6,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_7,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(apply(b,B),C)) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_9,plain,
apply(apply(t,A),apply(t,B)) = apply(A,B),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_6073,plain,
apply(f(A),apply(apply(t,g(A)),h(A))) != apply(apply(apply(A,f(A)),g(A)),h(A)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_16,plain,
apply(apply(apply(A,f(A)),g(A)),h(A)) != apply(f(A),apply(apply(t,g(A)),h(A))),
inference(copy,[status(thm)],[c_6073]) ).
cnf(c_6074,plain,
apply(apply(t,A),apply(B,C)) = apply(apply(apply(t,C),B),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_26,plain,
apply(apply(apply(t,A),B),C) = apply(apply(t,C),apply(B,A)),
inference(copy,[status(thm)],[c_6074]) ).
cnf(c_28,plain,
apply(apply(t,A),apply(apply(t,B),C)) = apply(apply(C,B),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_29,plain,
apply(A,apply(apply(apply(t,B),t),C)) = apply(A,apply(C,B)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_87,plain,
apply(apply(t,A),apply(apply(apply(t,B),b),C)) = apply(B,apply(C,A)),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_128,plain,
apply(apply(t,A),apply(apply(t,B),apply(b,C))) = apply(C,apply(B,A)),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_359,plain,
apply(apply(t,h(A)),apply(apply(A,f(A)),g(A))) != apply(f(A),apply(apply(t,g(A)),h(A))),
inference(paramod,[status(thm)],[c_2,c_16]) ).
cnf(c_6075,plain,
apply(apply(t,apply(A,B)),apply(t,C)) = apply(apply(apply(apply(t,B),t),A),C),
inference(paramod,[status(thm)],[c_29,c_9]) ).
cnf(c_6076,plain,
apply(apply(A,B),C) = apply(apply(apply(apply(t,B),t),A),C),
inference(paramod,[status(thm)],[c_9,c_6075]) ).
cnf(c_561,plain,
apply(apply(apply(apply(t,A),t),B),C) = apply(apply(B,A),C),
inference(copy,[status(thm)],[c_6076]) ).
cnf(c_2756,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(apply(t,apply(b,C)),b),D))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_87,c_8]) ).
cnf(c_3346,plain,
apply(apply(t,apply(A,B)),C) = apply(apply(t,B),apply(apply(t,A),apply(b,C))),
inference(paramod,[status(thm)],[c_128,c_2]) ).
cnf(c_3433,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_128,c_26]) ).
cnf(c_6077,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_128,c_561]) ).
cnf(c_6078,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_3433,c_6077]) ).
cnf(c_6079,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_3346,c_6078]) ).
cnf(c_6080,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_3346,c_6079]) ).
cnf(c_6081,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_3346,c_6080]) ).
cnf(c_6082,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_3346,c_6081]) ).
cnf(c_6083,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_3346,c_6082]) ).
cnf(c_3522,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_6083]) ).
cnf(c_6084,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(apply(t,C),apply(apply(t,b),apply(b,b))),D))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_3346,c_2756]) ).
cnf(c_6085,plain,
apply(apply(t,A),apply(apply(t,B),apply(apply(t,C),apply(apply(t,t),apply(apply(t,apply(apply(t,b),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,D)))))))))))))))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_3522,c_6084]) ).
cnf(c_6086,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,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,D)))))))))))))))))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_3346,c_6085]) ).
cnf(c_6087,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,b),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,D)))))))))))))))))))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_3346,c_6086]) ).
cnf(c_3813,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,b),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,D)))))))))))))))))))))) = apply(C,apply(apply(D,B),A)),
inference(paramod,[status(thm)],[c_3346,c_6087]) ).
cnf(c_6070,plain,
apply(apply(t,h(A)),apply(apply(t,g(A)),apply(apply(t,f(A)),A))) != apply(f(A),apply(apply(t,g(A)),h(A))),
inference(paramod,[status(thm)],[c_28,c_359]) ).
cnf(c_6071,plain,
$false,
inference(resolve,[status(thm)],[c_6070,c_3813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:07:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 725847 was started by sandbox on n007,
% 0.10/0.36 % Sat Sep 26 23:07:54 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 19.22/2.86
% 19.22/2.86 % SZS status Unsatisfiable for theBenchmark
% 19.22/2.86
% 19.22/2.86 % Proof 1 at 2.33 (+ 0.14) seconds.
% 19.22/2.86 % Length of proof is 24.
% 19.22/2.86 % Level of proof is 6.
% 19.22/2.86 % Maximum clause weight is 77.000.
% 19.22/2.86 % Given clauses 88.
% 19.22/2.86
% 19.22/2.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------