%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE011+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:44:04 AM UTC 2026
% Result : Theorem 2.03s 0.64s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 115 ( 75 unt; 0 def)
% Number of atoms : 185 ( 117 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 140 ( 70 ~; 53 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 117 ( 1 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(goals,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_22,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_23,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_24,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_25,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_27,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK0(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_28,plain,
( ~ complement(B,A)
| test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_29,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_30,plain,
( c(sK0(A)) = A
| ~ test(sK0(A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_31,plain,
( addition(A,sK0(A)) = one
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_32,plain,
( multiplication(sK0(A),A) = zero
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_33,plain,
( multiplication(A,sK0(A)) = zero
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_34,plain,
( c(B) != A
| ~ test(B)
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_35,plain,
( addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_38,plain,
( c(B) != A
| ~ test(B)
| addition(A,B) = one ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_42,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_43,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_45,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_47,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_48,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_49]) ).
fof(nnf_19,plain,
? [X0,X1] :
( addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) != one
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))) != one
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK2),skolemize(X1,sK1)],[nnf_19]) ).
cnf(c_56,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_58,negated_conjecture,
addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1313,negated_conjecture,
addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),c(sK1))) != one,
inference(paramod,[status(thm)],[c_40,c_58]) ).
cnf(c_59,negated_conjecture,
addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2))) != one,
inference(paramod,[status(thm)],[c_40,c_1313]) ).
cnf(c_64,plain,
( addition(B,A) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| test(A) ),
inference(paramod,[status(thm)],[c_40,c_35]) ).
cnf(c_1314,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_41]) ).
cnf(c_67,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_41,c_1314]) ).
cnf(c_69,negated_conjecture,
addition(multiplication(addition(sK2,c(sK2)),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2))) != one,
inference(paramod,[status(thm)],[c_67,c_59]) ).
cnf(c_1315,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_72,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_1315]) ).
cnf(c_1316,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_73,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_1316]) ).
cnf(c_78,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_48,c_41]) ).
cnf(c_83,plain,
addition(multiplication(addition(A,B),C),D) = addition(multiplication(A,C),addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_50,c_41]) ).
cnf(c_88,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))) != one,
inference(paramod,[status(thm)],[c_83,c_69]) ).
cnf(c_109,plain,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_56,c_38]) ).
cnf(c_112,plain,
( c(sK1) != A
| test(A) ),
inference(resolve,[status(thm)],[c_56,c_34]) ).
cnf(c_115,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_56,c_31]) ).
cnf(c_122,plain,
( c(sK2) != A
| addition(A,sK2) = one ),
inference(resolve,[status(thm)],[c_57,c_38]) ).
cnf(c_125,plain,
( c(sK2) != A
| test(A) ),
inference(resolve,[status(thm)],[c_57,c_34]) ).
cnf(c_1317,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_1318,plain,
test(addition(zero,c(sK1))),
inference(resolve,[status(thm)],[c_112,c_1317]) ).
cnf(c_180,plain,
test(c(sK1)),
inference(paramod,[status(thm)],[c_72,c_1318]) ).
cnf(c_192,plain,
multiplication(c(sK1),sK0(c(sK1))) = zero,
inference(resolve,[status(thm)],[c_180,c_33]) ).
cnf(c_193,plain,
multiplication(sK0(c(sK1)),c(sK1)) = zero,
inference(resolve,[status(thm)],[c_180,c_32]) ).
cnf(c_194,plain,
addition(c(sK1),sK0(c(sK1))) = one,
inference(resolve,[status(thm)],[c_180,c_31]) ).
cnf(c_1319,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_115,c_73]) ).
cnf(c_1320,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_40,c_1319]) ).
cnf(c_213,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_115,c_1320]) ).
cnf(c_1321,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_1322,plain,
test(addition(zero,c(sK2))),
inference(resolve,[status(thm)],[c_125,c_1321]) ).
cnf(c_259,plain,
test(c(sK2)),
inference(paramod,[status(thm)],[c_72,c_1322]) ).
cnf(c_288,plain,
multiplication(c(sK2),sK0(c(sK2))) = zero,
inference(resolve,[status(thm)],[c_259,c_33]) ).
cnf(c_289,plain,
multiplication(sK0(c(sK2)),c(sK2)) = zero,
inference(resolve,[status(thm)],[c_259,c_32]) ).
cnf(c_290,plain,
addition(c(sK2),sK0(c(sK2))) = one,
inference(resolve,[status(thm)],[c_259,c_31]) ).
cnf(c_1323,plain,
addition(multiplication(A,one),B) = addition(multiplication(A,one),addition(multiplication(A,sK1),B)),
inference(paramod,[status(thm)],[c_213,c_78]) ).
cnf(c_1324,plain,
addition(A,B) = addition(multiplication(A,one),addition(multiplication(A,sK1),B)),
inference(paramod,[status(thm)],[c_45,c_1323]) ).
cnf(c_1325,plain,
addition(A,B) = addition(A,addition(multiplication(A,sK1),B)),
inference(paramod,[status(thm)],[c_45,c_1324]) ).
cnf(c_316,plain,
addition(A,addition(multiplication(A,sK1),B)) = addition(A,B),
inference(copy,[status(thm)],[c_1325]) ).
cnf(c_1326,plain,
( multiplication(c(sK1),sK0(c(sK1))) != zero
| multiplication(sK0(c(sK1)),c(sK1)) != zero
| test(sK0(c(sK1))) ),
inference(resolve,[status(thm)],[c_194,c_64]) ).
cnf(c_1327,plain,
( multiplication(c(sK1),sK0(c(sK1))) != zero
| zero != zero
| test(sK0(c(sK1))) ),
inference(paramod,[status(thm)],[c_193,c_1326]) ).
cnf(c_1328,plain,
( zero != zero
| zero != zero
| test(sK0(c(sK1))) ),
inference(paramod,[status(thm)],[c_192,c_1327]) ).
cnf(c_1329,plain,
( zero != zero
| test(sK0(c(sK1))) ),
inference(copy,[status(thm)],[c_1328]) ).
cnf(c_665,plain,
test(sK0(c(sK1))),
inference(copy,[status(thm)],[c_1329]) ).
cnf(c_1330,plain,
( c(sK0(c(sK1))) = c(sK1)
| ~ test(c(sK1)) ),
inference(resolve,[status(thm)],[c_665,c_30]) ).
cnf(c_690,plain,
c(sK0(c(sK1))) = c(sK1),
inference(resolve,[status(thm)],[c_180,c_1330]) ).
cnf(c_1331,plain,
( multiplication(c(sK2),sK0(c(sK2))) != zero
| multiplication(sK0(c(sK2)),c(sK2)) != zero
| test(sK0(c(sK2))) ),
inference(resolve,[status(thm)],[c_290,c_64]) ).
cnf(c_1332,plain,
( multiplication(c(sK2),sK0(c(sK2))) != zero
| zero != zero
| test(sK0(c(sK2))) ),
inference(paramod,[status(thm)],[c_289,c_1331]) ).
cnf(c_1333,plain,
( zero != zero
| zero != zero
| test(sK0(c(sK2))) ),
inference(paramod,[status(thm)],[c_288,c_1332]) ).
cnf(c_1334,plain,
( zero != zero
| test(sK0(c(sK2))) ),
inference(copy,[status(thm)],[c_1333]) ).
cnf(c_871,plain,
test(sK0(c(sK2))),
inference(copy,[status(thm)],[c_1334]) ).
cnf(c_1335,plain,
( c(sK0(c(sK2))) = c(sK2)
| ~ test(c(sK2)) ),
inference(resolve,[status(thm)],[c_871,c_30]) ).
cnf(c_896,plain,
c(sK0(c(sK2))) = c(sK2),
inference(resolve,[status(thm)],[c_259,c_1335]) ).
cnf(c_1336,plain,
c(sK1) = c(sK0(c(sK1))),
inference(copy,[status(thm)],[c_690]) ).
cnf(c_1337,plain,
addition(c(sK0(c(sK1))),sK1) = one,
inference(resolve,[status(thm)],[c_109,c_1336]) ).
cnf(c_1338,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_690,c_1337]) ).
cnf(c_1231,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_1338]) ).
cnf(c_1339,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(one,sK2)))) != one,
inference(paramod,[status(thm)],[c_1231,c_88]) ).
cnf(c_1340,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),sK2))) != one,
inference(paramod,[status(thm)],[c_46,c_1339]) ).
cnf(c_1341,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(sK2,multiplication(c(sK2),c(sK1))))) != one,
inference(paramod,[status(thm)],[c_40,c_1340]) ).
cnf(c_1342,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,addition(multiplication(c(sK2),sK1),multiplication(c(sK2),c(sK1))))) != one,
inference(paramod,[status(thm)],[c_67,c_1341]) ).
cnf(c_1343,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),addition(sK1,c(sK1))))) != one,
inference(paramod,[status(thm)],[c_48,c_1342]) ).
cnf(c_1344,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),one))) != one,
inference(paramod,[status(thm)],[c_1231,c_1343]) ).
cnf(c_1345,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,c(sK2))) != one,
inference(paramod,[status(thm)],[c_45,c_1344]) ).
cnf(c_1346,negated_conjecture,
addition(sK2,addition(multiplication(sK2,sK1),c(sK2))) != one,
inference(paramod,[status(thm)],[c_67,c_1345]) ).
cnf(c_1232,negated_conjecture,
addition(sK2,c(sK2)) != one,
inference(paramod,[status(thm)],[c_316,c_1346]) ).
cnf(c_1347,plain,
c(sK2) = c(sK0(c(sK2))),
inference(copy,[status(thm)],[c_896]) ).
cnf(c_1348,plain,
addition(c(sK0(c(sK2))),sK2) = one,
inference(resolve,[status(thm)],[c_122,c_1347]) ).
cnf(c_1349,plain,
addition(c(sK2),sK2) = one,
inference(paramod,[status(thm)],[c_896,c_1348]) ).
cnf(c_1350,plain,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_40,c_1349]) ).
cnf(c_1312,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1232,c_1350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:15:22 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3912637 was started by sandbox on n002,
% 0.10/0.36 % Fri Sep 25 19:15:22 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 2.03/0.64
% 2.03/0.64 % SZS status Theorem for theBenchmark
% 2.03/0.64
% 2.03/0.64 % Proof 1 at 0.20 (+ 0.07) seconds.
% 2.03/0.64 % Length of proof is 71.
% 2.03/0.64 % Level of proof is 10.
% 2.03/0.64 % Maximum clause weight is 23.000.
% 2.03/0.64 % Given clauses 167.
% 2.03/0.64
% 2.03/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
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