%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:29:09 AM UTC 2026
% Result : Unsatisfiable 10.33s 1.85s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 2
% Syntax : Number of formulae : 140 ( 140 unt; 0 def)
% Number of atoms : 140 ( 139 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 : 18 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 609 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,inverse(multiply(multiply(multiply(inverse(VAR_1),VAR_1),inverse(multiply(inverse(multiply(VAR_0,inverse(VAR_1))),VAR_2))),VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_3,plain,
multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),multiply(inverse(multiply(B,inverse(C))),D)))),A)) = D,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_5,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_2961,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(C,inverse(D))),B))),D)))),E)))),A)) = E,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)) = C,
inference(paramod,[status(thm)],[c_1,c_2961]) ).
cnf(c_2962,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(inverse(multiply(multiply(multiply(inverse(inverse(C)),inverse(C)),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(inverse(C)))),multiply(inverse(multiply(D,inverse(E))),B)))),inverse(C))),F)))),A)) = F,
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_10,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C,
inference(paramod,[status(thm)],[c_8,c_2962]) ).
cnf(c_2963,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))) = multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),C))),D),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_11,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),C))),A) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(C,B)))),
inference(copy,[status(thm)],[c_2963]) ).
cnf(c_17,plain,
multiply(A,multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(C,inverse(inverse(B)))),multiply(C,A)))),inverse(multiply(multiply(multiply(inverse(B),B),inverse(D)),B)))) = D,
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_2964,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),C),B)))) = multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,C)))),D),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_18,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A) = multiply(inverse(multiply(D,inverse(E))),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),C),E)))),
inference(copy,[status(thm)],[c_2964]) ).
cnf(c_19,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_2965,plain,
multiply(inverse(A),multiply(B,C)) = multiply(inverse(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(B,inverse(E))),A))),E)))),multiply(D,C)),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_21,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)))),multiply(A,E)) = multiply(inverse(D),multiply(C,E)),
inference(copy,[status(thm)],[c_2965]) ).
cnf(c_2966,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(F,inverse(E))),multiply(F,B)))),E)))),multiply(D,C)),
inference(paramod,[status(thm)],[c_10,c_19]) ).
cnf(c_28,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_10,c_2966]) ).
cnf(c_2967,plain,
multiply(inverse(multiply(A,B)),C) = multiply(inverse(multiply(D,B)),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(A,inverse(E))),C))),E)))),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_32,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,B)),E),
inference(copy,[status(thm)],[c_2967]) ).
cnf(c_2968,plain,
multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),D)) = multiply(inverse(multiply(E,B)),multiply(E,D)),
inference(paramod,[status(thm)],[c_10,c_28]) ).
cnf(c_39,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(E,inverse(B))),multiply(E,D)))),C)),
inference(copy,[status(thm)],[c_2968]) ).
cnf(c_40,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_41,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_61,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,multiply(V6,C))),multiply(F,multiply(V6,E))),
inference(paramod,[status(thm)],[c_28,c_40]) ).
cnf(c_157,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(multiply(C,A)))))) = C,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_306,plain,
multiply(multiply(inverse(multiply(A,B)),multiply(A,B)),inverse(multiply(inverse(multiply(C,inverse(multiply(A,B)))),multiply(C,inverse(multiply(inverse(multiply(D,E)),multiply(D,B))))))) = inverse(multiply(A,E)),
inference(paramod,[status(thm)],[c_28,c_157]) ).
cnf(c_2969,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(A,B)),C)))),multiply(D,inverse(multiply(inverse(multiply(E,multiply(A,F))),multiply(E,C))))))) = inverse(multiply(inverse(multiply(V6,B)),multiply(V6,F))),
inference(paramod,[status(thm)],[c_40,c_157]) ).
cnf(c_310,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))),
inference(paramod,[status(thm)],[c_306,c_2969]) ).
cnf(c_2970,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A) = multiply(inverse(multiply(D,inverse(E))),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(F))),C))),F))),
inference(paramod,[status(thm)],[c_3,c_18]) ).
cnf(c_389,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),A) = C,
inference(paramod,[status(thm)],[c_1,c_2970]) ).
cnf(c_475,plain,
multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(C))))),D)),E)),multiply(inverse(multiply(F,D)),multiply(F,A))) = multiply(inverse(multiply(V6,E)),multiply(V6,C)),
inference(paramod,[status(thm)],[c_389,c_41]) ).
cnf(c_575,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(V6,V7)),multiply(V6,D)))),multiply(F,V8))) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_61,c_41]) ).
cnf(c_2971,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(B))),F))),inverse(C))),V6))),C)))) = multiply(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))),V6),
inference(paramod,[status(thm)],[c_3,c_32]) ).
cnf(c_2972,plain,
multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(E))),inverse(B))),F))),B)),V6) = multiply(multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E))),V6),
inference(paramod,[status(thm)],[c_32,c_2971]) ).
cnf(c_757,plain,
multiply(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),D) = multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(E))),C))),E)),D),
inference(copy,[status(thm)],[c_2972]) ).
cnf(c_2973,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C))))),multiply(inverse(multiply(F,B)),V6)) = multiply(inverse(multiply(inverse(multiply(D,V7)),E)),multiply(inverse(multiply(F,V7)),V6)),
inference(paramod,[status(thm)],[c_32,c_40]) ).
cnf(c_762,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(D,F)),E)),
inference(paramod,[status(thm)],[c_32,c_2973]) ).
cnf(c_2974,plain,
multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,D)),E)) = multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(F,inverse(D))),multiply(F,A)))),V6)),B)),multiply(inverse(multiply(C,V6)),E)),
inference(paramod,[status(thm)],[c_10,c_762]) ).
cnf(c_918,plain,
multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),D)),E)),multiply(inverse(multiply(F,D)),V6)) = multiply(inverse(multiply(C,E)),multiply(inverse(multiply(F,A)),V6)),
inference(copy,[status(thm)],[c_2974]) ).
cnf(c_1001,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,D)),multiply(C,D))) = multiply(inverse(multiply(E,B)),multiply(E,A)),
inference(paramod,[status(thm)],[c_918,c_475]) ).
cnf(c_2975,plain,
multiply(inverse(A),inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),B))) = multiply(inverse(multiply(D,E)),multiply(D,E)),
inference(paramod,[status(thm)],[c_1001,c_1]) ).
cnf(c_2976,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(D,E)),multiply(D,E)),
inference(paramod,[status(thm)],[c_10,c_2975]) ).
cnf(c_1006,plain,
multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(C),C),
inference(copy,[status(thm)],[c_2976]) ).
cnf(c_2977,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),multiply(D,inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(D,inverse(E))),C))),E))))) = multiply(inverse(multiply(F,B)),multiply(F,A)),
inference(paramod,[status(thm)],[c_1,c_1001]) ).
cnf(c_1010,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(paramod,[status(thm)],[c_1,c_2977]) ).
cnf(c_1118,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,B)))))),D)),multiply(inverse(multiply(E,F)),multiply(E,F))) = multiply(inverse(multiply(multiply(inverse(B),B),D)),C),
inference(paramod,[status(thm)],[c_157,c_1001]) ).
cnf(c_2978,plain,
multiply(inverse(A),multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(B,inverse(C))),A))),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_1,c_1006]) ).
cnf(c_1233,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1,c_2978]) ).
cnf(c_2979,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A) = multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(A)),D)))),
inference(paramod,[status(thm)],[c_1006,c_11]) ).
cnf(c_1281,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A) = A,
inference(paramod,[status(thm)],[c_5,c_2979]) ).
cnf(c_1403,plain,
multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(C))),D))),C))) = D,
inference(paramod,[status(thm)],[c_1233,c_1]) ).
cnf(c_1405,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_1233,c_2]) ).
cnf(c_1412,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,D)))),C)) = D,
inference(paramod,[status(thm)],[c_1233,c_10]) ).
cnf(c_1429,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),C))),A) = multiply(inverse(multiply(D,inverse(E))),multiply(D,inverse(multiply(C,E)))),
inference(paramod,[status(thm)],[c_1233,c_11]) ).
cnf(c_1443,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(multiply(D,C)))))) = D,
inference(paramod,[status(thm)],[c_1233,c_157]) ).
cnf(c_1460,plain,
multiply(A,multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(C,inverse(inverse(B)))),multiply(C,A)))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),B)))) = E,
inference(paramod,[status(thm)],[c_1233,c_17]) ).
cnf(c_1471,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(inverse(B)),inverse(A))),multiply(inverse(C),C)))),A) = B,
inference(paramod,[status(thm)],[c_1233,c_389]) ).
cnf(c_2980,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(C),inverse(B))),D))),B)))),multiply(A,C)) = multiply(inverse(D),multiply(inverse(E),E)),
inference(paramod,[status(thm)],[c_1233,c_21]) ).
cnf(c_1487,plain,
multiply(inverse(A),multiply(inverse(B),B)) = multiply(inverse(A),multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_21,c_2980]) ).
cnf(c_1664,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_1487,c_1233]) ).
cnf(c_1975,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(D),inverse(B))),multiply(inverse(multiply(inverse(E),E)),multiply(inverse(F),F))))),C)),
inference(paramod,[status(thm)],[c_1664,c_39]) ).
cnf(c_2981,plain,
multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(B,C)),D))),multiply(inverse(E),E)) = multiply(inverse(multiply(inverse(multiply(F,multiply(B,V6))),multiply(F,D))),multiply(inverse(multiply(inverse(multiply(V7,C)),multiply(V7,V6))),A)),
inference(paramod,[status(thm)],[c_40,c_1010]) ).
cnf(c_2187,plain,
multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,C))),V6)) = multiply(inverse(multiply(inverse(V6),multiply(inverse(multiply(B,F)),D))),multiply(inverse(V7),V7)),
inference(copy,[status(thm)],[c_2981]) ).
cnf(c_2330,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(D),D)) = multiply(inverse(multiply(E,multiply(inverse(F),F))),multiply(E,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_1010,c_1010]) ).
cnf(c_2334,plain,
multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),A) = multiply(inverse(multiply(D,C)),multiply(D,A)),
inference(paramod,[status(thm)],[c_1281,c_28]) ).
cnf(c_2982,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(F),F))),multiply(D,C))),E),
inference(paramod,[status(thm)],[c_1281,c_40]) ).
cnf(c_2341,plain,
multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,D))),A) = multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),multiply(inverse(multiply(C,F)),A)),
inference(copy,[status(thm)],[c_2982]) ).
cnf(c_2362,plain,
inverse(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),A)) = inverse(multiply(inverse(multiply(D,C)),multiply(D,A))),
inference(paramod,[status(thm)],[c_1281,c_310]) ).
cnf(c_2394,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C) = C,
inference(paramod,[status(thm)],[c_1233,c_1281]) ).
cnf(c_2983,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(B),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(D),D))),A)),
inference(paramod,[status(thm)],[c_1281,c_1010]) ).
cnf(c_2402,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_2394,c_2983]) ).
cnf(c_2984,plain,
inverse(multiply(inverse(C),A)) = inverse(multiply(inverse(multiply(D,C)),multiply(D,A))),
inference(paramod,[status(thm)],[c_2394,c_2362]) ).
cnf(c_2417,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(B),C)),
inference(copy,[status(thm)],[c_2984]) ).
cnf(c_2985,plain,
multiply(inverse(multiply(C,D)),A) = multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,D))),multiply(inverse(multiply(C,F)),A)),
inference(paramod,[status(thm)],[c_2394,c_2341]) ).
cnf(c_2986,plain,
multiply(inverse(multiply(C,D)),A) = multiply(inverse(multiply(inverse(F),D)),multiply(inverse(multiply(C,F)),A)),
inference(paramod,[status(thm)],[c_2417,c_2985]) ).
cnf(c_2422,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(C,B)),D),
inference(copy,[status(thm)],[c_2986]) ).
cnf(c_2987,plain,
multiply(inverse(C),A) = multiply(inverse(multiply(D,C)),multiply(D,A)),
inference(paramod,[status(thm)],[c_2394,c_2334]) ).
cnf(c_2424,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
inference(copy,[status(thm)],[c_2987]) ).
cnf(c_2988,plain,
multiply(inverse(multiply(inverse(B),C)),multiply(inverse(D),D)) = multiply(inverse(multiply(E,multiply(inverse(F),F))),multiply(E,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_2424,c_2330]) ).
cnf(c_2989,plain,
multiply(inverse(C),B) = multiply(inverse(multiply(E,multiply(inverse(F),F))),multiply(E,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_2402,c_2988]) ).
cnf(c_2990,plain,
multiply(inverse(C),B) = multiply(inverse(multiply(inverse(F),F)),multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_2424,c_2989]) ).
cnf(c_2428,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(B),C),
inference(copy,[status(thm)],[c_2990]) ).
cnf(c_2991,plain,
multiply(inverse(multiply(inverse(multiply(B,C)),D)),multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,C))),V6)) = multiply(inverse(multiply(inverse(V6),multiply(inverse(multiply(B,F)),D))),multiply(inverse(V7),V7)),
inference(paramod,[status(thm)],[c_2424,c_2187]) ).
cnf(c_2992,plain,
multiply(inverse(multiply(inverse(multiply(B,C)),D)),multiply(inverse(multiply(inverse(F),C)),V6)) = multiply(inverse(multiply(inverse(V6),multiply(inverse(multiply(B,F)),D))),multiply(inverse(V7),V7)),
inference(paramod,[status(thm)],[c_2424,c_2991]) ).
cnf(c_2438,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),E)) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),E),
inference(paramod,[status(thm)],[c_2402,c_2992]) ).
cnf(c_2993,plain,
multiply(inverse(B),C) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(D),inverse(B))),multiply(inverse(multiply(inverse(E),E)),multiply(inverse(F),F))))),C)),
inference(paramod,[status(thm)],[c_2424,c_1975]) ).
cnf(c_2994,plain,
multiply(inverse(B),C) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(inverse(D),inverse(B))),multiply(inverse(F),F)))),C)),
inference(paramod,[status(thm)],[c_2428,c_2993]) ).
cnf(c_2995,plain,
multiply(inverse(B),C) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(inverse(B)),D))),C)),
inference(paramod,[status(thm)],[c_2402,c_2994]) ).
cnf(c_2442,plain,
multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(inverse(B)),A))),C)) = multiply(inverse(B),C),
inference(copy,[status(thm)],[c_2995]) ).
cnf(c_2455,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),inverse(B)))),A) = B,
inference(paramod,[status(thm)],[c_2402,c_1471]) ).
cnf(c_2996,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))),D)),multiply(inverse(multiply(E,F)),multiply(E,F))) = multiply(inverse(multiply(multiply(inverse(B),B),D)),C),
inference(paramod,[status(thm)],[c_2424,c_1118]) ).
cnf(c_2997,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))),D)),multiply(inverse(F),F)) = multiply(inverse(multiply(multiply(inverse(B),B),D)),C),
inference(paramod,[status(thm)],[c_2424,c_2996]) ).
cnf(c_2998,plain,
multiply(inverse(D),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))) = multiply(inverse(multiply(multiply(inverse(B),B),D)),C),
inference(paramod,[status(thm)],[c_2402,c_2997]) ).
cnf(c_2466,plain,
multiply(inverse(multiply(multiply(inverse(A),A),B)),C) = multiply(inverse(B),inverse(multiply(inverse(inverse(A)),inverse(multiply(C,A))))),
inference(copy,[status(thm)],[c_2998]) ).
cnf(c_2999,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(V6,V7)),multiply(V6,D)))),multiply(F,V8))) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_2424,c_575]) ).
cnf(c_3000,plain,
multiply(inverse(multiply(inverse(multiply(inverse(C),D)),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(V6,V7)),multiply(V6,D)))),multiply(F,V8))) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_2424,c_2999]) ).
cnf(c_3001,plain,
multiply(inverse(multiply(inverse(multiply(inverse(C),D)),E)),multiply(inverse(multiply(F,multiply(inverse(V7),D))),multiply(F,V8))) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_2424,c_3000]) ).
cnf(c_3002,plain,
multiply(inverse(multiply(inverse(multiply(inverse(C),D)),E)),multiply(inverse(multiply(inverse(V7),D)),V8)) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_2424,c_3001]) ).
cnf(c_3003,plain,
multiply(inverse(multiply(inverse(multiply(inverse(C),V7)),E)),V8) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(multiply(V10,V7)),multiply(V10,C))),V8))),
inference(paramod,[status(thm)],[c_2438,c_3002]) ).
cnf(c_3004,plain,
multiply(inverse(multiply(inverse(multiply(inverse(C),V7)),E)),V8) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(inverse(multiply(inverse(V7),C)),V8))),
inference(paramod,[status(thm)],[c_2424,c_3003]) ).
cnf(c_2504,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),D) = multiply(inverse(C),multiply(inverse(multiply(inverse(B),A)),D)),
inference(paramod,[status(thm)],[c_2424,c_3004]) ).
cnf(c_3005,plain,
multiply(A,multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(inverse(inverse(B))),A))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),B)))) = E,
inference(paramod,[status(thm)],[c_2424,c_1460]) ).
cnf(c_2526,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),A))) = C,
inference(paramod,[status(thm)],[c_2442,c_3005]) ).
cnf(c_2532,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))) = C,
inference(paramod,[status(thm)],[c_2424,c_1443]) ).
cnf(c_2535,plain,
inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(B)),C))),B)) = C,
inference(paramod,[status(thm)],[c_2424,c_1412]) ).
cnf(c_3006,plain,
multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(inverse(A)),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))))),A) = multiply(inverse(multiply(D,inverse(E))),multiply(D,inverse(multiply(C,E)))),
inference(paramod,[status(thm)],[c_2466,c_1429]) ).
cnf(c_3007,plain,
multiply(inverse(inverse(B)),inverse(multiply(C,B))) = multiply(inverse(multiply(D,inverse(E))),multiply(D,inverse(multiply(C,E)))),
inference(paramod,[status(thm)],[c_2455,c_3006]) ).
cnf(c_2581,plain,
multiply(inverse(inverse(A)),inverse(multiply(B,A))) = multiply(inverse(inverse(C)),inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_2424,c_3007]) ).
cnf(c_2599,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(B),B))) = multiply(inverse(inverse(C)),inverse(multiply(inverse(A),C))),
inference(paramod,[status(thm)],[c_1233,c_2581]) ).
cnf(c_2601,plain,
multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,A)))),multiply(inverse(inverse(C)),D)) = multiply(inverse(inverse(multiply(B,C))),D),
inference(paramod,[status(thm)],[c_2581,c_2424]) ).
cnf(c_2602,plain,
multiply(inverse(multiply(inverse(inverse(A)),B)),multiply(inverse(inverse(C)),inverse(multiply(D,C)))) = multiply(inverse(B),inverse(multiply(D,A))),
inference(paramod,[status(thm)],[c_2581,c_2424]) ).
cnf(c_3008,plain,
multiply(multiply(inverse(A),A),B) = multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),inverse(D))),inverse(C))),E))),C)),B),
inference(paramod,[status(thm)],[c_1233,c_757]) ).
cnf(c_3009,plain,
multiply(multiply(inverse(A),A),B) = multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(C)),multiply(inverse(multiply(inverse(inverse(D)),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D)))),E)))),C)),B),
inference(paramod,[status(thm)],[c_2504,c_3008]) ).
cnf(c_3010,plain,
multiply(multiply(inverse(A),A),B) = multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(C)),multiply(inverse(E),E)))),C)),B),
inference(paramod,[status(thm)],[c_2526,c_3009]) ).
cnf(c_2619,plain,
multiply(multiply(inverse(A),A),B) = multiply(multiply(inverse(C),C),B),
inference(paramod,[status(thm)],[c_2535,c_3010]) ).
cnf(c_3011,plain,
multiply(inverse(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),A)))),multiply(inverse(inverse(B)),C)) = multiply(inverse(inverse(multiply(inverse(D),D))),C),
inference(paramod,[status(thm)],[c_2599,c_2424]) ).
cnf(c_2706,plain,
multiply(inverse(inverse(multiply(inverse(A),A))),B) = multiply(inverse(inverse(multiply(inverse(C),C))),B),
inference(paramod,[status(thm)],[c_2601,c_3011]) ).
cnf(c_3012,plain,
multiply(inverse(multiply(inverse(inverse(A)),B)),multiply(inverse(inverse(C)),inverse(multiply(inverse(A),C)))) = multiply(inverse(B),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_2599,c_2424]) ).
cnf(c_2707,plain,
multiply(inverse(A),inverse(multiply(inverse(B),B))) = multiply(inverse(A),inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_2602,c_3012]) ).
cnf(c_2731,plain,
multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_2707,c_1233]) ).
cnf(c_2732,plain,
multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))),a2) != a2,
inference(paramod,[status(thm)],[c_2707,c_1405]) ).
cnf(c_2844,plain,
multiply(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C))))),a2) != a2,
inference(paramod,[status(thm)],[c_2707,c_2732]) ).
cnf(c_2845,plain,
multiply(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(D),D))))),a2) != a2,
inference(paramod,[status(thm)],[c_2707,c_2844]) ).
cnf(c_2850,plain,
multiply(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(E),E))))),a2) != a2,
inference(paramod,[status(thm)],[c_2707,c_2845]) ).
cnf(c_2878,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),A))),B)),multiply(inverse(inverse(multiply(inverse(C),C))),D)) = multiply(inverse(B),D),
inference(paramod,[status(thm)],[c_2706,c_2424]) ).
cnf(c_2904,plain,
multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))) = inverse(multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_2731,c_2532]) ).
cnf(c_3013,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),A))),B)),multiply(inverse(inverse(multiply(inverse(C),C))),D)) = multiply(inverse(multiply(multiply(inverse(E),E),B)),D),
inference(paramod,[status(thm)],[c_2904,c_2422]) ).
cnf(c_3014,plain,
multiply(inverse(B),D) = multiply(inverse(multiply(multiply(inverse(E),E),B)),D),
inference(paramod,[status(thm)],[c_2878,c_3013]) ).
cnf(c_3015,plain,
multiply(inverse(B),D) = multiply(inverse(B),inverse(multiply(inverse(inverse(E)),inverse(multiply(D,E))))),
inference(paramod,[status(thm)],[c_2466,c_3014]) ).
cnf(c_2916,plain,
multiply(inverse(A),inverse(multiply(inverse(inverse(B)),inverse(multiply(C,B))))) = multiply(inverse(A),C),
inference(copy,[status(thm)],[c_3015]) ).
cnf(c_2945,plain,
multiply(inverse(multiply(multiply(inverse(A),A),B)),C) = multiply(inverse(B),C),
inference(paramod,[status(thm)],[c_2916,c_2466]) ).
cnf(c_3016,plain,
A = multiply(multiply(inverse(B),B),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(multiply(inverse(D),D),inverse(E))),A))),E))),
inference(paramod,[status(thm)],[c_1403,c_2619]) ).
cnf(c_3017,plain,
A = multiply(multiply(inverse(B),B),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(inverse(E)),A))),E))),
inference(paramod,[status(thm)],[c_2945,c_3016]) ).
cnf(c_3018,plain,
A = multiply(multiply(inverse(B),B),A),
inference(paramod,[status(thm)],[c_2535,c_3017]) ).
cnf(c_2959,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(copy,[status(thm)],[c_3018]) ).
cnf(c_2960,plain,
$false,
inference(resolve,[status(thm)],[c_2959,c_2850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n015.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:56:13 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1654537 was started by sandbox on n015,
% 0.17/0.43 % Fri Sep 25 14:56:13 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 10.33/1.85
% 10.33/1.85 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 10.33/1.85
% 10.33/1.85 % SZS status Unsatisfiable for theBenchmark
% 10.33/1.85
% 10.33/1.85 % Proof 1 at 1.03 (+ 0.29) seconds.
% 10.33/1.85 % Length of proof is 80.
% 10.33/1.85 % Level of proof is 24.
% 10.33/1.85 % Maximum clause weight is 100.000.
% 10.33/1.85 % Given clauses 97.
% 10.33/1.85
% 10.33/1.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------