%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 06:49:07 AM UTC 2026
% Result : Unsatisfiable 90.47s 21.97s
% Output : CNFRefutation 90.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 98 ( 34 unt; 0 def)
% Number of atoms : 190 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 144 ( 52 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f_is_associative,axiom,
! [VAR_0,VAR_1,VAR_2] : f(VAR_0,f(VAR_1,VAR_2)) = f(f(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',f_is_associative) ).
cnf(c_1,plain,
f(A,f(B,C)) = f(f(A,B),C),
inference(clausify,[status(thm)],[f_is_associative]) ).
cnf(c_2,plain,
f(f(A,B),C) = f(A,f(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(partitions_union,axiom,
! [VAR_0] :
( d2(VAR_0)
| d1(VAR_0)
| c(VAR_0) ),
file('theBenchmark.p',partitions_union) ).
cnf(c_3,plain,
( d2(A)
| d1(A)
| c(A) ),
inference(clausify,[status(thm)],[partitions_union]) ).
fof(partitions_exclusive_c_d1,axiom,
! [VAR_0] :
( ~ d1(VAR_0)
| ~ c(VAR_0) ),
file('theBenchmark.p',partitions_exclusive_c_d1) ).
cnf(c_4,plain,
( ~ d1(A)
| ~ c(A) ),
inference(clausify,[status(thm)],[partitions_exclusive_c_d1]) ).
fof(partitions_exclusive_c_d2,axiom,
! [VAR_0] :
( ~ d2(VAR_0)
| ~ c(VAR_0) ),
file('theBenchmark.p',partitions_exclusive_c_d2) ).
cnf(c_5,plain,
( ~ d2(A)
| ~ c(A) ),
inference(clausify,[status(thm)],[partitions_exclusive_c_d2]) ).
fof(partition_d1_not_empty,axiom,
d1(a2),
file('theBenchmark.p',partition_d1_not_empty) ).
cnf(c_8,plain,
d1(a2),
inference(clausify,[status(thm)],[partition_d1_not_empty]) ).
fof(partition_d2_not_empty,axiom,
d2(a3),
file('theBenchmark.p',partition_d2_not_empty) ).
cnf(c_9,plain,
d2(a3),
inference(clausify,[status(thm)],[partition_d2_not_empty]) ).
fof(conjecture_1,axiom,
! [VAR_0,VAR_1] :
( ~ c(VAR_1)
| ~ c(VAR_0)
| d1(f(VAR_0,VAR_1))
| d2(f(VAR_0,VAR_1)) ),
file('theBenchmark.p',conjecture_1) ).
cnf(c_10,plain,
( ~ c(B)
| ~ c(A)
| d1(f(A,B))
| d2(f(A,B)) ),
inference(clausify,[status(thm)],[conjecture_1]) ).
fof(conjecture_2,axiom,
! [VAR_0,VAR_1] :
( ~ d1(VAR_1)
| ~ d1(VAR_0)
| c(f(VAR_0,VAR_1)) ),
file('theBenchmark.p',conjecture_2) ).
cnf(c_11,plain,
( ~ d1(B)
| ~ d1(A)
| c(f(A,B)) ),
inference(clausify,[status(thm)],[conjecture_2]) ).
fof(conjecture_3,axiom,
! [VAR_0,VAR_1] :
( ~ d2(VAR_1)
| ~ d2(VAR_0)
| c(f(VAR_0,VAR_1)) ),
file('theBenchmark.p',conjecture_3) ).
cnf(c_12,plain,
( ~ d2(B)
| ~ d2(A)
| c(f(A,B)) ),
inference(clausify,[status(thm)],[conjecture_3]) ).
cnf(c_13,plain,
( ~ c(A)
| d1(f(A,A))
| d2(f(A,A)) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_14,plain,
( ~ d1(A)
| c(f(A,A)) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_15,plain,
( ~ d2(A)
| c(f(A,A)) ),
inference(factor,[status(thm)],[c_12]) ).
cnf(c_18,plain,
~ c(a2),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_24,plain,
( ~ d1(A)
| c(f(a2,A)) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_25,plain,
( ~ d1(A)
| c(f(A,a2)) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_28,plain,
( ~ d2(A)
| c(f(A,a3)) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_31,plain,
c(f(a2,a2)),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_32,plain,
c(f(a3,a3)),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_33,plain,
( d1(A)
| c(A)
| c(f(A,A)) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_10717,plain,
( d1(f(f(a2,a2),f(a2,a2)))
| d2(f(f(a2,a2),f(a2,a2))) ),
inference(resolve,[status(thm)],[c_31,c_13]) ).
cnf(c_10718,plain,
( d1(f(f(a2,a2),f(a2,a2)))
| d2(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10717]) ).
cnf(c_34,plain,
( d1(f(a2,f(a2,f(a2,a2))))
| d2(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10718]) ).
cnf(c_10719,plain,
( ~ c(A)
| d1(f(f(a2,a2),A))
| d2(f(f(a2,a2),A)) ),
inference(resolve,[status(thm)],[c_31,c_10]) ).
cnf(c_10720,plain,
( ~ c(A)
| d1(f(f(a2,a2),A))
| d2(f(a2,f(a2,A))) ),
inference(paramod,[status(thm)],[c_2,c_10719]) ).
cnf(c_36,plain,
( ~ c(A)
| d1(f(a2,f(a2,A)))
| d2(f(a2,f(a2,A))) ),
inference(paramod,[status(thm)],[c_2,c_10720]) ).
cnf(c_45,plain,
( d1(A)
| c(A)
| c(f(A,a3)) ),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_10721,plain,
( c(f(A,A))
| c(A)
| c(f(A,A)) ),
inference(resolve,[status(thm)],[c_33,c_14]) ).
cnf(c_54,plain,
( c(A)
| c(f(A,A)) ),
inference(copy,[status(thm)],[c_10721]) ).
cnf(c_10722,plain,
( ~ c(B)
| d1(f(f(A,A),B))
| d2(f(f(A,A),B))
| c(A) ),
inference(resolve,[status(thm)],[c_54,c_10]) ).
cnf(c_10723,plain,
( ~ c(B)
| d1(f(f(A,A),B))
| d2(f(A,f(A,B)))
| c(A) ),
inference(paramod,[status(thm)],[c_2,c_10722]) ).
cnf(c_60,plain,
( ~ c(B)
| d1(f(A,f(A,B)))
| d2(f(A,f(A,B)))
| c(A) ),
inference(paramod,[status(thm)],[c_2,c_10723]) ).
cnf(c_61,plain,
( c(f(A,B))
| c(f(A,f(B,f(A,B)))) ),
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_67,plain,
( c(f(a2,A))
| c(A)
| c(f(A,a3)) ),
inference(resolve,[status(thm)],[c_45,c_24]) ).
cnf(c_10724,plain,
( c(f(f(a2,f(a2,f(a2,a2))),a3))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(resolve,[status(thm)],[c_34,c_28]) ).
cnf(c_10725,plain,
( c(f(a2,f(f(a2,f(a2,a2)),a3)))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10724]) ).
cnf(c_10726,plain,
( c(f(a2,f(a2,f(f(a2,a2),a3))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10725]) ).
cnf(c_89,plain,
( c(f(a2,f(a2,f(a2,f(a2,a3)))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10726]) ).
cnf(c_10727,plain,
( c(f(f(a2,f(a2,f(a2,a2))),f(a2,f(a2,f(a2,a2)))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(resolve,[status(thm)],[c_34,c_15]) ).
cnf(c_10728,plain,
( c(f(a2,f(f(a2,f(a2,a2)),f(a2,f(a2,f(a2,a2))))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10727]) ).
cnf(c_10729,plain,
( c(f(a2,f(a2,f(f(a2,a2),f(a2,f(a2,f(a2,a2)))))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10728]) ).
cnf(c_92,plain,
( c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2))))))))
| d1(f(a2,f(a2,f(a2,a2)))) ),
inference(paramod,[status(thm)],[c_2,c_10729]) ).
cnf(c_128,plain,
( c(f(a2,f(A,B)))
| c(f(A,B))
| c(f(A,f(B,a3))) ),
inference(paramod,[status(thm)],[c_2,c_67]) ).
cnf(c_155,plain,
( d1(f(a2,f(a2,f(a3,a3))))
| d2(f(a2,f(a2,f(a3,a3)))) ),
inference(resolve,[status(thm)],[c_36,c_32]) ).
cnf(c_10730,plain,
( c(f(f(A,B),C))
| c(f(f(A,B),f(C,f(A,f(B,C))))) ),
inference(paramod,[status(thm)],[c_2,c_61]) ).
cnf(c_10731,plain,
( c(f(f(A,B),C))
| c(f(A,f(B,f(C,f(A,f(B,C)))))) ),
inference(paramod,[status(thm)],[c_2,c_10730]) ).
cnf(c_195,plain,
( c(f(A,f(B,C)))
| c(f(A,f(B,f(C,f(A,f(B,C)))))) ),
inference(paramod,[status(thm)],[c_2,c_10731]) ).
cnf(c_10732,plain,
( c(f(f(a2,f(a2,f(a2,a2))),a2))
| c(f(a2,f(a2,f(a2,f(a2,a3))))) ),
inference(resolve,[status(thm)],[c_89,c_25]) ).
cnf(c_10733,plain,
( c(f(a2,f(f(a2,f(a2,a2)),a2)))
| c(f(a2,f(a2,f(a2,f(a2,a3))))) ),
inference(paramod,[status(thm)],[c_2,c_10732]) ).
cnf(c_10734,plain,
( c(f(a2,f(a2,f(f(a2,a2),a2))))
| c(f(a2,f(a2,f(a2,f(a2,a3))))) ),
inference(paramod,[status(thm)],[c_2,c_10733]) ).
cnf(c_888,plain,
( c(f(a2,f(a2,f(a2,f(a2,a2)))))
| c(f(a2,f(a2,f(a2,f(a2,a3))))) ),
inference(paramod,[status(thm)],[c_2,c_10734]) ).
cnf(c_10735,plain,
( c(f(f(a2,f(a2,f(a2,a2))),f(a2,f(a2,f(a2,a2)))))
| c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))) ),
inference(resolve,[status(thm)],[c_92,c_14]) ).
cnf(c_10736,plain,
( c(f(a2,f(f(a2,f(a2,a2)),f(a2,f(a2,f(a2,a2))))))
| c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))) ),
inference(paramod,[status(thm)],[c_2,c_10735]) ).
cnf(c_10737,plain,
( c(f(a2,f(a2,f(f(a2,a2),f(a2,f(a2,f(a2,a2)))))))
| c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))) ),
inference(paramod,[status(thm)],[c_2,c_10736]) ).
cnf(c_10738,plain,
( c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2))))))))
| c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))) ),
inference(paramod,[status(thm)],[c_2,c_10737]) ).
cnf(c_1237,plain,
c(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))),
inference(copy,[status(thm)],[c_10738]) ).
cnf(c_1369,plain,
( ~ c(f(a2,f(a2,f(a3,a3))))
| d1(f(a2,f(a2,f(a3,a3)))) ),
inference(resolve,[status(thm)],[c_155,c_5]) ).
cnf(c_7269,plain,
~ d2(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))),
inference(resolve,[status(thm)],[c_5,c_1237]) ).
cnf(c_7270,plain,
~ d1(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))),
inference(resolve,[status(thm)],[c_4,c_1237]) ).
cnf(c_10739,plain,
( ~ c(A)
| d1(f(a2,f(a2,A)))
| d2(f(a2,f(a2,A))) ),
inference(resolve,[status(thm)],[c_60,c_18]) ).
cnf(c_10740,plain,
( ~ c(f(a2,f(a2,f(a2,f(a2,f(a2,a2))))))
| d1(f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))))) ),
inference(resolve,[status(thm)],[c_10739,c_7269]) ).
cnf(c_7510,plain,
~ c(f(a2,f(a2,f(a2,f(a2,f(a2,a2)))))),
inference(resolve,[status(thm)],[c_10740,c_7270]) ).
cnf(c_7520,plain,
~ d1(f(a2,f(a2,f(a2,f(a2,a2))))),
inference(resolve,[status(thm)],[c_24,c_7510]) ).
cnf(c_9911,plain,
c(f(a2,f(a2,a2))),
inference(resolve,[status(thm)],[c_195,c_7510]) ).
cnf(c_10741,plain,
( d1(f(a2,f(a2,f(a2,f(a2,a2)))))
| d2(f(a2,f(a2,f(a2,f(a2,a2))))) ),
inference(resolve,[status(thm)],[c_9911,c_36]) ).
cnf(c_9960,plain,
d2(f(a2,f(a2,f(a2,f(a2,a2))))),
inference(resolve,[status(thm)],[c_7520,c_10741]) ).
cnf(c_10742,plain,
c(f(f(a2,f(a2,f(a2,f(a2,a2)))),a3)),
inference(resolve,[status(thm)],[c_9960,c_28]) ).
cnf(c_10743,plain,
c(f(a2,f(f(a2,f(a2,f(a2,a2))),a3))),
inference(paramod,[status(thm)],[c_2,c_10742]) ).
cnf(c_10744,plain,
c(f(a2,f(a2,f(f(a2,f(a2,a2)),a3)))),
inference(paramod,[status(thm)],[c_2,c_10743]) ).
cnf(c_10745,plain,
c(f(a2,f(a2,f(a2,f(f(a2,a2),a3))))),
inference(paramod,[status(thm)],[c_2,c_10744]) ).
cnf(c_9980,plain,
c(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))),
inference(paramod,[status(thm)],[c_2,c_10745]) ).
cnf(c_9986,plain,
~ c(f(a2,f(a2,f(a2,f(a2,a2))))),
inference(resolve,[status(thm)],[c_9960,c_5]) ).
cnf(c_9998,plain,
c(f(a2,f(a2,f(a2,f(a2,a3))))),
inference(resolve,[status(thm)],[c_9986,c_888]) ).
cnf(c_10341,plain,
~ d2(f(a2,f(a2,f(a2,f(a2,a3))))),
inference(resolve,[status(thm)],[c_5,c_9998]) ).
cnf(c_10342,plain,
~ d1(f(a2,f(a2,f(a2,f(a2,a3))))),
inference(resolve,[status(thm)],[c_4,c_9998]) ).
cnf(c_10502,plain,
~ d2(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))),
inference(resolve,[status(thm)],[c_5,c_9980]) ).
cnf(c_10503,plain,
~ d1(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))),
inference(resolve,[status(thm)],[c_4,c_9980]) ).
cnf(c_10746,plain,
( ~ c(A)
| d1(f(a2,f(a2,A)))
| d2(f(a2,f(a2,A))) ),
inference(resolve,[status(thm)],[c_60,c_18]) ).
cnf(c_10747,plain,
( ~ c(f(a2,f(a2,a3)))
| d1(f(a2,f(a2,f(a2,f(a2,a3))))) ),
inference(resolve,[status(thm)],[c_10746,c_10341]) ).
cnf(c_10538,plain,
~ c(f(a2,f(a2,a3))),
inference(resolve,[status(thm)],[c_10747,c_10342]) ).
cnf(c_10748,plain,
( ~ c(A)
| d1(f(a2,f(a2,A)))
| d2(f(a2,f(a2,A))) ),
inference(resolve,[status(thm)],[c_60,c_18]) ).
cnf(c_10749,plain,
( ~ c(f(a2,f(a2,f(a2,a3))))
| d1(f(a2,f(a2,f(a2,f(a2,f(a2,a3)))))) ),
inference(resolve,[status(thm)],[c_10748,c_10502]) ).
cnf(c_10665,plain,
~ c(f(a2,f(a2,f(a2,a3)))),
inference(resolve,[status(thm)],[c_10749,c_10503]) ).
cnf(c_10750,plain,
( c(f(a2,f(a2,a3)))
| c(f(a2,f(f(a2,a3),a3))) ),
inference(resolve,[status(thm)],[c_10665,c_128]) ).
cnf(c_10751,plain,
( c(f(a2,f(a2,a3)))
| c(f(a2,f(a2,f(a3,a3)))) ),
inference(paramod,[status(thm)],[c_2,c_10750]) ).
cnf(c_10674,plain,
c(f(a2,f(a2,f(a3,a3)))),
inference(resolve,[status(thm)],[c_10538,c_10751]) ).
cnf(c_10676,plain,
d1(f(a2,f(a2,f(a3,a3)))),
inference(resolve,[status(thm)],[c_10674,c_1369]) ).
cnf(c_10752,plain,
~ d1(f(a2,f(a2,f(a3,a3)))),
inference(resolve,[status(thm)],[c_4,c_10674]) ).
cnf(c_10716,plain,
$false,
inference(resolve,[status(thm)],[c_10676,c_10752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n002.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 21:01:17 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 2691193 was started by sandbox2 on n002,
% 0.11/10.39 % Sat Sep 26 21:01:17 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 90.47/21.97
% 90.47/21.97 % SZS status Unsatisfiable for theBenchmark
% 90.47/21.97
% 90.47/21.97 % Proof 1 at 10.80 (+ 0.56) seconds.
% 90.47/21.97 % Length of proof is 53.
% 90.47/21.97 % Level of proof is 16.
% 90.47/21.97 % Maximum clause weight is 24.000.
% 90.47/21.97 % Given clauses 300.
% 90.47/21.97
% 90.47/21.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
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