TSTP Solution File: KLE138+1 by ConnectPP---0.2.2
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% File : ConnectPP---0.2.2
% Problem : KLE138+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Mar 6 09:07:32 EST 2024
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE138+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Mar 4 11:14:27 EST 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Formula: additive_commutativity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(additive_commutativity-1, axiom, ( ( addition(_u1, _u0) = addition(_u0, _u1)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: additive_associativity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(additive_associativity-1, axiom, ( ( addition(_u2, addition(_u3, _u4)) = addition(addition(_u2, _u3), _u4)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: additive_identity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(additive_identity-1, axiom, ( ( addition(_u5, zero) = _u5) )).
% 0.12/0.37
% 0.12/0.37 % Formula: idempotence ( axiom ) converted to clauses:
% 0.12/0.37 cnf(idempotence-1, axiom, ( ( addition(_u6, _u6) = _u6) )).
% 0.12/0.37
% 0.12/0.37 % Formula: multiplicative_associativity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(multiplicative_associativity-1, axiom, ( ( multiplication(_u9, multiplication(_u8, _u7)) = multiplication(multiplication(_u9, _u8), _u7)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: multiplicative_right_identity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(multiplicative_right_identity-1, axiom, ( ( multiplication(_u10, one) = _u10) )).
% 0.12/0.37
% 0.12/0.37 % Formula: multiplicative_left_identity ( axiom ) converted to clauses:
% 0.12/0.37 cnf(multiplicative_left_identity-1, axiom, ( ( multiplication(one, _u11) = _u11) )).
% 0.12/0.37
% 0.12/0.37 % Formula: distributivity1 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(distributivity1-1, axiom, ( ( multiplication(_u14, addition(_u13, _u12)) = addition(multiplication(_u14, _u13), multiplication(_u14, _u12))) )).
% 0.12/0.37
% 0.12/0.37 % Formula: distributivity2 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(distributivity2-1, axiom, ( ( multiplication(addition(_u17, _u16), _u15) = addition(multiplication(_u17, _u15), multiplication(_u16, _u15))) )).
% 0.12/0.37
% 0.12/0.37 % Formula: left_annihilation ( axiom ) converted to clauses:
% 0.12/0.37 cnf(left_annihilation-1, axiom, ( ( multiplication(zero, _u18) = zero) )).
% 0.12/0.37
% 0.12/0.37 % Formula: star_unfold1 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(star_unfold1-1, axiom, ( ( addition(one, multiplication(_u19, star(_u19))) = star(_u19)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: star_unfold2 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(star_unfold2-1, axiom, ( ( addition(one, multiplication(star(_u20), _u20)) = star(_u20)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: star_induction1 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(star_induction1-1, axiom, ( ~leq(addition(multiplication(_u23, _u21), _u22), _u21) | leq(multiplication(star(_u23), _u22), _u21) )).
% 0.12/0.37
% 0.12/0.37 % Formula: star_induction2 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(star_induction2-1, axiom, ( ~leq(addition(multiplication(_u24, _u26), _u25), _u24) | leq(multiplication(_u25, star(_u26)), _u24) )).
% 0.12/0.37
% 0.12/0.37 % Formula: infty_unfold1 ( axiom ) converted to clauses:
% 0.12/0.37 cnf(infty_unfold1-1, axiom, ( ( strong_iteration(_u27) = addition(multiplication(_u27, strong_iteration(_u27)), one)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: infty_coinduction ( axiom ) converted to clauses:
% 0.12/0.37 cnf(infty_coinduction-1, axiom, ( ~leq(_u28, addition(multiplication(_u30, _u28), _u29)) | leq(_u28, multiplication(strong_iteration(_u30), _u29)) )).
% 0.12/0.37
% 0.12/0.37 % Formula: isolation ( axiom ) converted to clauses:
% 0.12/0.37 cnf(isolation-1, axiom, ( ( strong_iteration(_u31) = addition(star(_u31), multiplication(strong_iteration(_u31), zero))) )).
% 0.12/0.37
% 0.12/0.37 % Formula: order ( axiom ) converted to clauses:
% 0.12/0.37 cnf(order-1, axiom, ( ~leq(_u36, _u34) | ( addition(_u36, _u34) = _u34) )).
% 0.12/0.37 cnf(order-2, axiom, ( ( addition(_u37, _u35) != _u35) | leq(_u37, _u35) )).
% 0.12/0.37
% 0.12/0.37 % Formula: goals ( conjecture ) converted to clauses:
% 0.12/0.37 cnf(goals-1, negated_conjecture, ( ( strong_iteration(zero) != one) )).
% 0.12/0.37
% 0.12/0.37 % Problem matrix:
% 0.12/0.37 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.12/0.37 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.12/0.37 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.12/0.37 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( addition(__eqx_0, __eqx_1) = addition(__eqy_0, __eqy_1)) )).
% 0.12/0.37 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( multiplication(__eqx_0, __eqx_1) = multiplication(__eqy_0, __eqy_1)) )).
% 0.12/0.37 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( star(__eqx_0) = star(__eqy_0)) )).
% 0.12/0.37 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( strong_iteration(__eqx_0) = strong_iteration(__eqy_0)) )).
% 0.12/0.37 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~leq(__eqx_0, __eqx_1) | leq(__eqy_0, __eqy_1) )).
% 0.12/0.37 cnf(matrix-8, plain, ( ( addition(_u1, _u0) = addition(_u0, _u1)) )).
% 0.12/0.37 cnf(matrix-9, plain, ( ( addition(_u2, addition(_u3, _u4)) = addition(addition(_u2, _u3), _u4)) )).
% 0.12/0.37 cnf(matrix-10, plain, ( ( addition(_u5, zero) = _u5) )).
% 0.12/0.37 cnf(matrix-11, plain, ( ( addition(_u6, _u6) = _u6) )).
% 0.12/0.37 cnf(matrix-12, plain, ( ( multiplication(_u9, multiplication(_u8, _u7)) = multiplication(multiplication(_u9, _u8), _u7)) )).
% 0.12/0.37 cnf(matrix-13, plain, ( ( multiplication(_u10, one) = _u10) )).
% 0.12/0.37 cnf(matrix-14, plain, ( ( multiplication(one, _u11) = _u11) )).
% 0.12/0.37 cnf(matrix-15, plain, ( ( multiplication(_u14, addition(_u13, _u12)) = addition(multiplication(_u14, _u13), multiplication(_u14, _u12))) )).
% 0.12/0.37 cnf(matrix-16, plain, ( ( multiplication(addition(_u17, _u16), _u15) = addition(multiplication(_u17, _u15), multiplication(_u16, _u15))) )).
% 0.12/0.37 cnf(matrix-17, plain, ( ( multiplication(zero, _u18) = zero) )).
% 0.12/0.37 cnf(matrix-18, plain, ( ( addition(one, multiplication(_u19, star(_u19))) = star(_u19)) )).
% 0.12/0.37 cnf(matrix-19, plain, ( ( addition(one, multiplication(star(_u20), _u20)) = star(_u20)) )).
% 0.12/0.37 cnf(matrix-20, plain, ( ~leq(addition(multiplication(_u23, _u21), _u22), _u21) | leq(multiplication(star(_u23), _u22), _u21) )).
% 0.12/0.37 cnf(matrix-21, plain, ( ~leq(addition(multiplication(_u24, _u26), _u25), _u24) | leq(multiplication(_u25, star(_u26)), _u24) )).
% 0.12/0.37 cnf(matrix-22, plain, ( ( strong_iteration(_u27) = addition(multiplication(_u27, strong_iteration(_u27)), one)) )).
% 0.12/0.37 cnf(matrix-23, plain, ( ~leq(_u28, addition(multiplication(_u30, _u28), _u29)) | leq(_u28, multiplication(strong_iteration(_u30), _u29)) )).
% 0.12/0.37 cnf(matrix-24, plain, ( ( strong_iteration(_u31) = addition(star(_u31), multiplication(strong_iteration(_u31), zero))) )).
% 0.12/0.37 cnf(matrix-25, plain, ( ~leq(_u36, _u34) | ( addition(_u36, _u34) = _u34) )).
% 0.12/0.37 cnf(matrix-26, plain, ( ( addition(_u37, _u35) != _u35) | leq(_u37, _u35) )).
% 0.12/0.37 cnf(matrix-27, plain, ( ( strong_iteration(zero) != one) )).
% 0.12/0.37
% 0.12/0.37 % Proof stack:
% 0.12/0.37 cnf(proof-stack, plain,
% 0.12/0.37 proof_stack(
% 0.12/0.37 start(27),
% 0.12/0.37 left_branch(0, 2, 2, 2),
% 0.12/0.37 left_branch(0, 22, 0, 3),
% 0.12/0.37 right_branch(3),
% 0.12/0.37 left_branch(0, 2, 2, 4),
% 0.12/0.37 left_branch(0, 3, 2, 5),
% 0.12/0.37 left_branch(0, 17, 0, 6),
% 0.12/0.37 right_branch(6),
% 0.12/0.37 left_branch(0, 0, 0, 7),
% 0.12/0.37 right_branch(7),
% 0.12/0.37 right_branch(5),
% 0.12/0.37 left_branch(0, 2, 2, 6),
% 0.12/0.37 left_branch(0, 8, 0, 7),
% 0.12/0.37 right_branch(7),
% 0.12/0.37 left_branch(0, 10, 0, 8),
% 0.12/0.37 right_branch(8),
% 0.12/0.37 right_branch(6),
% 0.12/0.37 right_branch(4),
% 0.12/0.37 right_branch(2)
% 0.12/0.37 )).
% 0.12/0.37 % SZS output end Proof for theBenchmark
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