%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:44:17 AM UTC 2026
% Result : Unsatisfiable 216.12s 29.11s
% Output : CNFRefutation 216.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 4 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [VAR_0,VAR_1] : addition(VAR_0,VAR_1) = addition(VAR_1,VAR_0),
file('theBenchmark.p',additive_commutativity) ).
cnf(c_3,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
fof(additive_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : addition(VAR_0,addition(VAR_1,VAR_2)) = addition(addition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',additive_associativity) ).
cnf(c_4,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_5,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(copy,[status(thm)],[c_4]) ).
fof(additive_identity,axiom,
! [VAR_0] : addition(VAR_0,zero) = VAR_0,
file('theBenchmark.p',additive_identity) ).
cnf(c_6,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
fof(additive_idempotence,axiom,
! [VAR_0] : addition(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',additive_idempotence) ).
cnf(c_7,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
fof(multiplicative_right_identity,axiom,
! [VAR_0] : multiplication(VAR_0,one) = VAR_0,
file('theBenchmark.p',multiplicative_right_identity) ).
cnf(c_10,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
fof(multiplicative_left_identity,axiom,
! [VAR_0] : multiplication(one,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_left_identity) ).
cnf(c_11,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
fof(right_distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(VAR_0,addition(VAR_1,VAR_2)) = addition(multiplication(VAR_0,VAR_1),multiplication(VAR_0,VAR_2)),
file('theBenchmark.p',right_distributivity) ).
cnf(c_12,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_13,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_12]) ).
fof(left_distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiplication(addition(VAR_0,VAR_1),VAR_2) = addition(multiplication(VAR_0,VAR_2),multiplication(VAR_1,VAR_2)),
file('theBenchmark.p',left_distributivity) ).
cnf(c_14,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_15,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_14]) ).
fof(domain1,axiom,
! [VAR_0] : multiplication(antidomain(VAR_0),VAR_0) = zero,
file('theBenchmark.p',domain1) ).
cnf(c_20,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
fof(domain2,axiom,
! [VAR_0,VAR_1] : addition(antidomain(multiplication(VAR_0,VAR_1)),antidomain(multiplication(VAR_0,antidomain(antidomain(VAR_1))))) = antidomain(multiplication(VAR_0,antidomain(antidomain(VAR_1)))),
file('theBenchmark.p',domain2) ).
cnf(c_21,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(clausify,[status(thm)],[domain2]) ).
fof(domain3,axiom,
! [VAR_0] : addition(antidomain(antidomain(VAR_0)),antidomain(VAR_0)) = one,
file('theBenchmark.p',domain3) ).
cnf(c_22,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_23,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_3,c_22]) ).
fof(goals,axiom,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
file('theBenchmark.p',goals) ).
cnf(c_30,plain,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
inference(clausify,[status(thm)],[goals]) ).
cnf(c_31,plain,
addition(sK1_goals_X1,sK2_goals_X0) = sK1_goals_X1,
inference(paramod,[status(thm)],[c_3,c_30]) ).
fof(goals_1,axiom,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
file('theBenchmark.p',goals_1) ).
cnf(c_32,plain,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
inference(clausify,[status(thm)],[goals_1]) ).
cnf(c_30698,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_35,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_30698]) ).
cnf(c_30699,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_36,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_30699]) ).
cnf(c_39,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_13,c_5]) ).
cnf(c_30700,plain,
zero = antidomain(one),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_60,plain,
antidomain(one) = zero,
inference(copy,[status(thm)],[c_30700]) ).
cnf(c_30701,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_30702,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(A,B)),
inference(paramod,[status(thm)],[c_35,c_30701]) ).
cnf(c_61,plain,
multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_30702]) ).
cnf(c_30703,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_30704,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_3,c_30703]) ).
cnf(c_30705,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_35,c_30704]) ).
cnf(c_62,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_30705]) ).
cnf(c_30706,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_20,c_15]) ).
cnf(c_30707,plain,
multiplication(A,B) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_35,c_30706]) ).
cnf(c_63,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(copy,[status(thm)],[c_30707]) ).
cnf(c_30708,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_60,c_23]) ).
cnf(c_30709,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_60,c_30708]) ).
cnf(c_115,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_35,c_30709]) ).
cnf(c_30710,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_23,c_36]) ).
cnf(c_30711,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_3,c_30710]) ).
cnf(c_144,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_23,c_30711]) ).
cnf(c_30712,plain,
addition(multiplication(one,A),multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_144,c_15]) ).
cnf(c_30713,plain,
addition(A,multiplication(antidomain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_11,c_30712]) ).
cnf(c_156,plain,
addition(A,multiplication(antidomain(B),A)) = A,
inference(paramod,[status(thm)],[c_11,c_30713]) ).
cnf(c_30714,plain,
addition(multiplication(A,one),B) = addition(multiplication(A,antidomain(C)),addition(multiplication(A,antidomain(antidomain(C))),B)),
inference(paramod,[status(thm)],[c_23,c_39]) ).
cnf(c_30715,plain,
addition(A,B) = addition(multiplication(A,antidomain(C)),addition(multiplication(A,antidomain(antidomain(C))),B)),
inference(paramod,[status(thm)],[c_10,c_30714]) ).
cnf(c_194,plain,
addition(multiplication(A,antidomain(B)),addition(multiplication(A,antidomain(antidomain(B))),C)) = addition(A,C),
inference(copy,[status(thm)],[c_30715]) ).
cnf(c_30716,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_23,c_63]) ).
cnf(c_30717,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_11,c_30716]) ).
cnf(c_881,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_30717]) ).
cnf(c_30718,plain,
multiplication(antidomain(sK1_goals_X1),sK1_goals_X1) = multiplication(antidomain(sK1_goals_X1),sK2_goals_X0),
inference(paramod,[status(thm)],[c_31,c_61]) ).
cnf(c_30719,plain,
zero = multiplication(antidomain(sK1_goals_X1),sK2_goals_X0),
inference(paramod,[status(thm)],[c_20,c_30718]) ).
cnf(c_936,plain,
multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero,
inference(copy,[status(thm)],[c_30719]) ).
cnf(c_30720,plain,
addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(paramod,[status(thm)],[c_936,c_21]) ).
cnf(c_30721,plain,
addition(one,antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(paramod,[status(thm)],[c_115,c_30720]) ).
cnf(c_30722,plain,
one = antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(paramod,[status(thm)],[c_144,c_30721]) ).
cnf(c_957,plain,
antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = one,
inference(copy,[status(thm)],[c_30722]) ).
cnf(c_30723,plain,
multiplication(antidomain(antidomain(antidomain(A))),one) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_23,c_62]) ).
cnf(c_30724,plain,
antidomain(antidomain(antidomain(A))) = multiplication(antidomain(antidomain(antidomain(A))),antidomain(A)),
inference(paramod,[status(thm)],[c_10,c_30723]) ).
cnf(c_1001,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_881,c_30724]) ).
cnf(c_30725,plain,
multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = zero,
inference(paramod,[status(thm)],[c_957,c_20]) ).
cnf(c_1181,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = zero,
inference(paramod,[status(thm)],[c_11,c_30725]) ).
cnf(c_30726,plain,
addition(zero,addition(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(antidomain(sK2_goals_X0)))),A)) = addition(antidomain(sK1_goals_X1),A),
inference(paramod,[status(thm)],[c_1181,c_194]) ).
cnf(c_30727,plain,
addition(zero,addition(multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),A)) = addition(antidomain(sK1_goals_X1),A),
inference(paramod,[status(thm)],[c_1001,c_30726]) ).
cnf(c_6253,plain,
addition(multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),A) = addition(antidomain(sK1_goals_X1),A),
inference(paramod,[status(thm)],[c_35,c_30727]) ).
cnf(c_30728,plain,
addition(antidomain(sK1_goals_X1),zero) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(paramod,[status(thm)],[c_6253,c_6]) ).
cnf(c_30729,plain,
addition(zero,antidomain(sK1_goals_X1)) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(paramod,[status(thm)],[c_3,c_30728]) ).
cnf(c_30730,plain,
antidomain(sK1_goals_X1) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(paramod,[status(thm)],[c_35,c_30729]) ).
cnf(c_30689,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1),
inference(copy,[status(thm)],[c_30730]) ).
cnf(c_30731,plain,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = antidomain(sK2_goals_X0),
inference(paramod,[status(thm)],[c_30689,c_156]) ).
cnf(c_30696,plain,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0),
inference(paramod,[status(thm)],[c_3,c_30731]) ).
cnf(c_30697,plain,
$false,
inference(resolve,[status(thm)],[c_30696,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.64 % Computer : n018.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Fri Sep 25 19:22:52 UTC 2026
% 0.17/0.64 % CPUTime :
% 0.17/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.64 % Process 2634344 was started by sandbox2 on n018,
% 0.17/0.64 % Fri Sep 25 19:22:52 2026
% 0.17/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.65
% 0.21/0.65 % From the command line: assign(max_seconds, 300).
% 216.12/29.11
% 216.12/29.11 % given #500 (T,wt=9): 9438 leq(coantidomain(antidomain(A)),antidomain(antidomain(A))) = true. [para(1696(a,1),214(a,1,1))].
% 216.12/29.11
% 216.12/29.11 % given #1000 (T,wt=12): 2353 multiplication(antidomain(multiplication(addition(A,one),B)),multiplication(B,C)) = zero. [para(46(a,2),1025(a,1,1,1))].
% 216.12/29.11
% 216.12/29.11 % SZS status Unsatisfiable for theBenchmark
% 216.12/29.11
% 216.12/29.11 % Proof 1 at 22.21 (+ 6.11) seconds.
% 216.12/29.11 % Length of proof is 38.
% 216.12/29.11 % Level of proof is 9.
% 216.12/29.11 % Maximum clause weight is 18.000.
% 216.12/29.11 % Given clauses 1240.
% 216.12/29.11
% 216.12/29.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------