%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:26:18 AM UTC 2026
% Result : Unsatisfiable 2.07s 0.74s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 41 unt; 0 def)
% Number of atoms : 155 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 163 ( 86 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(closure_of_multiplication,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(c_3,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_6,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(associativity_of_addition1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(c_7,plain,
( sum(A,E,F)
| ~ sum(C,D,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition1]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_12,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_2,VAR_4,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity2) ).
cnf(c_13,plain,
( product(A,F,V6)
| ~ sum(C,E,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity2]) ).
fof(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ sum(VAR_0,VAR_1,VAR_3)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c_16,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(b_plus_inverse_c,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('theBenchmark.p',b_plus_inverse_c) ).
cnf(c_18,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(clausify,[status(thm)],[b_plus_inverse_c]) ).
fof(a_times_b,axiom,
product(a,b,aPb),
file('theBenchmark.p',a_times_b) ).
cnf(c_19,plain,
product(a,b,aPb),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_times_c,axiom,
product(a,c,aPc),
file('theBenchmark.p',a_times_c) ).
cnf(c_20,plain,
product(a,c,aPc),
inference(clausify,[status(thm)],[a_times_c]) ).
fof(aPb_plus_IaPc,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('theBenchmark.p',aPb_plus_IaPc) ).
cnf(c_21,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(clausify,[status(thm)],[aPb_plus_IaPc]) ).
fof(prove_a_times_bS_Ic_is_aPb_S__IaPc,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(c_22,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(clausify,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c_3382,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_3383,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_3382,c_4]) ).
cnf(c_29,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_3383,c_1]) ).
cnf(c_3384,plain,
( sum(add(D,A),B,E)
| ~ sum(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_3385,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_3384,c_5]) ).
cnf(c_77,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_3385,c_2]) ).
cnf(c_3386,plain,
( additive_identity = B
| ~ sum(additive_inverse(A),A,B) ),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_3387,plain,
additive_identity = add(additive_inverse(A),A),
inference(resolve,[status(thm)],[c_3386,c_4]) ).
cnf(c_119,plain,
add(additive_inverse(A),A) = additive_identity,
inference(copy,[status(thm)],[c_3387]) ).
cnf(c_3388,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_120,plain,
add(A,additive_identity) = A,
inference(resolve,[status(thm)],[c_3388,c_2]) ).
cnf(c_3389,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_121,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_3389,c_1]) ).
cnf(c_3390,plain,
( sum(aPb,B,D)
| ~ product(a,C,D)
| ~ sum(b,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_12,c_19]) ).
cnf(c_3391,plain,
( sum(aPb,multiply(a,A),C)
| ~ product(a,B,C)
| ~ sum(b,A,B) ),
inference(resolve,[status(thm)],[c_3390,c_3]) ).
cnf(c_3392,plain,
( sum(aPb,multiply(a,additive_identity),A)
| ~ product(a,b,A) ),
inference(resolve,[status(thm)],[c_3391,c_2]) ).
cnf(c_163,plain,
sum(aPb,multiply(a,additive_identity),aPb),
inference(resolve,[status(thm)],[c_3392,c_19]) ).
cnf(c_3393,plain,
( sum(aPb_S_IaPc,A,C)
| ~ sum(aPb,B,C)
| ~ sum(additive_inverse(aPc),A,B) ),
inference(resolve,[status(thm)],[c_8,c_21]) ).
cnf(c_3394,plain,
( sum(aPb_S_IaPc,aPc,A)
| ~ sum(aPb,additive_identity,A) ),
inference(resolve,[status(thm)],[c_3393,c_5]) ).
cnf(c_3395,plain,
sum(aPb_S_IaPc,aPc,add(aPb,additive_identity)),
inference(resolve,[status(thm)],[c_3394,c_4]) ).
cnf(c_222,plain,
sum(aPb_S_IaPc,aPc,aPb),
inference(paramod,[status(thm)],[c_120,c_3395]) ).
cnf(c_3396,plain,
( product(a,C,D)
| ~ sum(aPb,B,D)
| ~ sum(b,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_13,c_19]) ).
cnf(c_3397,plain,
( product(a,B,C)
| ~ sum(aPb,multiply(a,A),C)
| ~ sum(b,A,B) ),
inference(resolve,[status(thm)],[c_3396,c_3]) ).
cnf(c_3398,plain,
( product(a,bS_Ic,A)
| ~ sum(aPb,multiply(a,additive_inverse(c)),A) ),
inference(resolve,[status(thm)],[c_3397,c_18]) ).
cnf(c_233,plain,
~ sum(aPb,multiply(a,additive_inverse(c)),aPb_S_IaPc),
inference(resolve,[status(thm)],[c_3398,c_22]) ).
cnf(c_3399,plain,
( sum(aPb,A,C)
| ~ sum(aPb_S_IaPc,B,C)
| ~ sum(aPc,A,B) ),
inference(resolve,[status(thm)],[c_8,c_222]) ).
cnf(c_3400,plain,
( sum(aPb,A,B)
| ~ sum(aPc,A,add(additive_inverse(aPb_S_IaPc),B)) ),
inference(resolve,[status(thm)],[c_3399,c_29]) ).
cnf(c_3401,plain,
~ sum(aPc,multiply(a,additive_inverse(c)),add(additive_inverse(aPb_S_IaPc),aPb_S_IaPc)),
inference(resolve,[status(thm)],[c_3400,c_233]) ).
cnf(c_620,plain,
~ sum(aPc,multiply(a,additive_inverse(c)),additive_identity),
inference(paramod,[status(thm)],[c_119,c_3401]) ).
cnf(c_3402,plain,
( sum(aPc,B,D)
| ~ product(a,C,D)
| ~ sum(c,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_3403,plain,
( sum(aPc,multiply(a,A),C)
| ~ product(a,B,C)
| ~ sum(c,A,B) ),
inference(resolve,[status(thm)],[c_3402,c_3]) ).
cnf(c_3404,plain,
( sum(aPc,multiply(a,additive_inverse(c)),A)
| ~ product(a,additive_identity,A) ),
inference(resolve,[status(thm)],[c_3403,c_6]) ).
cnf(c_669,plain,
~ product(a,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_3404,c_620]) ).
cnf(c_3405,plain,
( product(A,E,F)
| ~ sum(multiply(A,D),C,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_3406,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_3405,c_3]) ).
cnf(c_3407,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),multiply(A,additive_identity),C) ),
inference(resolve,[status(thm)],[c_3406,c_2]) ).
cnf(c_768,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_3407,c_669]) ).
cnf(c_3408,plain,
( sum(add(D,additive_inverse(A)),C,E)
| ~ sum(D,B,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_77]) ).
cnf(c_3409,plain,
( sum(add(A,additive_inverse(aPb)),aPb,B)
| ~ sum(A,multiply(a,additive_identity),B) ),
inference(resolve,[status(thm)],[c_3408,c_163]) ).
cnf(c_3410,plain,
sum(add(additive_identity,additive_inverse(aPb)),aPb,multiply(a,additive_identity)),
inference(resolve,[status(thm)],[c_3409,c_1]) ).
cnf(c_3363,plain,
sum(additive_inverse(aPb),aPb,multiply(a,additive_identity)),
inference(paramod,[status(thm)],[c_121,c_3410]) ).
cnf(c_3411,plain,
( sum(B,multiply(a,additive_identity),C)
| ~ sum(A,aPb,C)
| ~ sum(A,aPb,B) ),
inference(resolve,[status(thm)],[c_8,c_163]) ).
cnf(c_3412,plain,
( sum(B,multiply(a,additive_identity),A)
| ~ sum(add(A,additive_inverse(aPb)),aPb,B) ),
inference(resolve,[status(thm)],[c_3411,c_77]) ).
cnf(c_3413,plain,
~ sum(add(additive_identity,additive_inverse(aPb)),aPb,multiply(a,additive_identity)),
inference(resolve,[status(thm)],[c_3412,c_768]) ).
cnf(c_3380,plain,
~ sum(additive_inverse(aPb),aPb,multiply(a,additive_identity)),
inference(paramod,[status(thm)],[c_121,c_3413]) ).
cnf(c_3381,plain,
$false,
inference(resolve,[status(thm)],[c_3380,c_3363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 05:47:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3266354 was started by sandbox2 on n015,
% 0.09/0.36 % Sat Sep 26 05:47:13 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 2.07/0.74
% 2.07/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.07/0.74
% 2.07/0.74 % Proof 1 at 0.24 (+ 0.09) seconds.
% 2.07/0.74 % Length of proof is 30.
% 2.07/0.74 % Level of proof is 7.
% 2.07/0.74 % Maximum clause weight is 25.000.
% 2.07/0.74 % Given clauses 74.
% 2.07/0.74
% 2.07/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------